I also live abroad so have some experience of navigating this.
I would ask your paediatrician or family doctor whether there is any support you can be referred for, for example occupational therapy (often called a variation on ergotherapy in some of the European languages) can often help with ADHD type challenges. Or a behaviour analyst can sometimes go into school to observe what patterns are contributing to the behaviour and might be able to suggest things which could help. Sometimes also children who are struggling at school can access help from a special needs/learning support teacher or assistant who can come in and liase with the class teacher and other staff who may be involved with your child. How to access this varies but it might be through the school themselves, through the doctor, or some other organisation.
You should also look up what children's rights are to access education where you are. Many countries have legislation about education needing to be accessible to all pupils regardless of need/diagnosis specifically, so if he is struggling to access education, then he may be covered by this kind of law. You should be able to see from this legislation who is responsible for ensuring this - whether it is the school themselves, any specific person at the school (e.g. head teacher, local equivalent of SENCo, pastoral care type role, school social worker) or some other authority such as the education authority, youth authority/children's services/disability services/health service or doctor, etc.
What you've specifically said:
he finds it very difficult to start tasks
Could you break this down at all - is it that he's struggling to follow multi-step directions? Does he know what to do, but gets stuck with the actual momentum, some kind of anxiety/perfectionism? Or he doesn't know what to do and where to start? How are they usually given a task - are they expected to be self-motivated, is it predictable/the same every time (e.g. continue with your work book)? Could he be paired with another pupil so that the other pupil can show him what he is supposed to be doing (if this isn't disrupting the other pupil) Could he be given written/typed instructions, or encouraged to write down the steps of what to do while the teacher is explaining it, rather than having to remember this verbally? He could use an extra notebook for this, to save making a mess in his normal book. If they are given a list of tasks or problems on paper or in a workbook, it can help for him to take a spare piece of plain paper and cover up all but the task he's currently working on.
is easily distracted.
Sometimes things like ear defenders or headphones can help with this, or being seated away from other pupils (although this can be stigmatising so I would hope it would be presented to him as a way to help him.) At age 10, the classroom ought to be a bit calmer than the classes for younger children, but if his class is especially rowdy, it might help for him to be able to do some work in another class which is quieter, or somewhere else like the library.
His attention span is very short
Often with ADHD it helps to have lots of smaller bits of reinforcement to be able to see progress, rather than waiting for a big bit of reinforcement at the end. This can essentially be delayed development of the "reward" part of the brain, so you might need to do more frequent reinforcement for smaller things like you would with younger children. With things like tasks, it can sometimes help to have something like a checklist so he can check things off as he does them, which will give him a sense of having achieved something especially if the teacher or a TA can occasionally go around and not just praise his work but also praise the fact he's ticked off some tasks and he's doing really well, keep it up. (And vv especially - if they could avoid making comments about how little he has done, and just focus on praising what he has done right, that helps a lot.)
Something offered to DS2 was a picture with various "dots" on the picture to colour in after e.g. a set number of tasks, or after using a sand timer to work on a task for a certain period of time without getting distracted - when he had a full sheet of dots completed, he could swap it for a small prize or reward e.g. 5 mins access to a certain toy. Something like a pomodoro timer can also work well - so he does a certain period where he's meant to be focusing on work and then he can have a short break, this can help, although they might need to experiment with the timings. As he is 10, it might be that he is considered old/sensible enough to be allowed to take short breaks when he needs them e.g. to leave the classroom and sit outside or quietly in a corridor.
he gets up frequently and moves around class
Some people with ADHD have a higher need for vestibular or proprioceptive (both fancy words for movement) input than average and find it difficult to focus/concentrate without this, or the movement might be a reaction to low arousal (essentially, low energy levels/lethargy) and an attempt to wake himself up and give himself the energy to complete his work. There are various seating options which can sometimes help with this - wobble cushions, sitting on a yoga ball or a wobble stool, for example. Though this can make things worse if he's getting up because he's uncomfortable sitting due to poor core strength. Resistance bands on his chair can also be a good way to fidget/get some proprioceptive input without it being disruptive to other children. Another option here might be movement breaks - essentially send him off to run laps of the playground for example, or have a whole-class movement break (there are LOADS of videos designed for use in schools, which are a short dance/exercise type break which can help a lot of children). Sometimes you can also do this sort of proactively e.g. find a way to add movement to his morning routine - could you walk, cycle or jog to school if you don't already? And do some kind of physical activity after school and at the weekends. This really helps my youngest the most (he is too young to know if he has ADHD but the older two do) - if he doesn't get enough exercise, then the following day or two his focus and behaviour is all over the place. But it can be hard to balance. DS2 cycles to school and this often helps him but sometimes when everything is stressful for some reason (e.g. out of routine due to end of term madness) adding the cycling is too much, and it works better if they can go to school on the tram instead.
plays with anything on his desk.
Another "some people with ADHD" one - but some people find that they can actually concentrate or listen better when they have another form of input going on. This could be the movement such as the wobble cushion mentioned before, but fidgeting can also be a way to try to get this input as well. This one can be tricky because sometimes children are distracted by things they are fidgeting with and this is taking their attention away from where it should be, but sometimes it is genuinely helping and it's just that they are not displaying the kind of body language we usually associate with listening/paying attention. This will probably depend on whether his teacher(s) is/are amenable to the idea that children can pay attention while looking away or moving their body/hands. Some don't seem to believe this is possible, or they just find it irritating and want to stop it anyway. But this kind of thing, if it is something which helps your DS and it is something the teacher is open to, can be a great accommodation - DS1 at age 10 used to doodle on every inch of his school work, and spend ages getting out his collection of approximately 30 novelty erasers and put them all onto his desk at once - when his teacher brought out the box of erasers to show them to me I was completely mortified 😅 he'd been receiving them as birthday/Christmas/random gifts from an enthusiastic aunt and I just assumed that he instantly lost most of them, but actually he was bringing them to school to be some kind of emotional support posse. Anyway, we agreed that up to 2 erasers would be a sensible number, and the rest could stay at home but I also asked if it would be OK for him to have a spare/plain exercise book to doodle in to keep the doodles out of his normal books and she did agree, and this was a really great solution for him for the last 2 years of primary school.
Some fidget toys are designed to be quiet for use in school (though a lot are not) and a really simple and effective one is often just a blob of putty, or blu-tak (which you can buy on amazon if it's not available in stores).
Often work is unfinished.
You might not be able to do much about this without a diagnosis if it's affecting his grades, as they might not be able to adjust grading. If it doesn't matter long term, I would probably pick your battles and celebrate his hard work at the end of the year rather than a particular grade. If it does matter, e.g. for next school entrance, see if there is any flexibility e.g. whether him having demonstrated the skill is enough rather than having to repeat it 10x. If there is something which is making him slower, like writing speed, it might be that you can look into some kind of assistive tech e.g. a laptop (more likely at secondary school in many countries). If it's causing him to fall behind because he isn't grasping the topic, private tutoring can help and because it's 1:1 it can be that you can find someone who makes it more engaging for him.
Is this causing problems e.g. issues with grades or stress for DS ie do they make him bring it all home as homework and it's taking up too much time? I have found sometimes, it's better to ask for forgiveness than permission, ie if I go in and try to make an arrangement about not doing the homework, it doesn't go down very well, but if I just stop accommodating it and don't make him, the whole thing will go away much more quickly. (It's not actually homework we've had issues with, so this could be about something else.) I know this sounds terrible, it's something you'll have to play by ear with the specific school and the system, but if your child is seriously struggling at school, it is often genuinely a case of juggling what you are willing to let go of on their end, what you have to let go of on your end and what you're able to try to communicate about, and none of it will be ideal either from their POV or yours. I also think sometimes they can be fairly rigid in what they are allowed to officially agree to, but they also deal with all manner of parents, some of whom are significantly less cooperative than me, and provided it's not a child protection issue, the bar they are willing to clear to get parents to comply with things is pretty low.