Exactly the same for both DS1 and DS2 who were 10 years apart.
I used to think it was just normal 3yo stuff and then I had DS3 who is like on easy mode in comparison 
and even he is referred to as "a little wildling" by some of the nursery staff! He is a dream though 
he does absolutely need a daily walk, but it actually succeeds in tiring him out.
Anyway, um, given it's way too early to query any kind of diagnosis, what to do to actually cope... nursery is amazing so make as much use of this as you can.
Playdates are good, but you'll probably have to suss out the ideal length before he gets overstimulated and silly.
Brain games, as well. I think unlike DS3 who has an abundance of physical energy which can be exhausted, my older two both have an abundance of mental energy, and so many thoughts that they are spilling out of them at all times. So at 3 thinking about what kinds of things would work to help occupy some of this.
Marble Rush is great and a 3yo can build most of it with only a bit of help.
Simple lego sets starting around age 4 building up to a larger collection as they get older. Rebrickable website is great for rebuilding and creativity value.
Any kind of sensory play like dry rice/lentils in a tray to sift through - if you do this on a tuff tray or just a smaller tray inside a large tray on a towel, it simplifies clean up. Anything arty/with different textures too like cheap shaving foam and food colouring. If you don't have outside space, do it in the bath.
Wooden train tracks have been a huge hit with both of them as well. At 3 I would help build the track but then I'd leave them to it to play. As they got older, they started to build more elaborate tracks themselves.
If you have interested but geographically far relatives, try video calls. It relieves some of the chatting burden and it's great for their relationship so if/when they come and visit they have that solid base which is lovely.
An old phone (all other functions locked off) or cheap/kids' camera with which they can video themselves or what they are doing.
Books are good - although you have to read them, it's great to get them really into the idea of exploring books and it helps motivate them when it's time to learn to read and then if they can read to themselves, that's brilliant. We have never bit the bullet on the cost, but I think in hindsight a Tonie box or similar would have been really worth the money as well. Another thing we only discovered really late is those books you can buy in supermarkets and WHSmith, The Works etc which have little homework-type exercises in them. I probably avoided them because I felt they were for people who want to hothouse their DC but honestly DS2/3 absolutely LOVE these especially the ones which have an opportunity to get a star on each page and I probably should have embraced them sooner.
If you do screen time - just be very careful with it. Try to avoid the temptation to give them free rein, especially of things like youtube. I have found with DS2 it's SO MUCH better when I say OK, you can watch [1/2/3] episodes of X and then it's a set amount of time and it goes off. It's so tempting to hand them the TV remote or a tablet and then zone out yourself, especially if it's the only thing that actually makes them stop talking, but it's an incredibly hard habit to break and especially with a child who has this kind of 100mph brain and difficulty in self-starting, IME. I am not saying do 0 TV, because it is a blessed relief but I do wish I had been more intentional with it from the start. Or maybe we all start out like that and creep into bad habits anyway. I just know that I constantly feel myself slipping into letting it take over and then it's really hard to pull it back once they have got used to that as an expectation, but it is much smoother when we all have the expectation that screens go on for a specific activity for a set time period and then stop. On games - some games can be good and fulfil the "brain exercise" function but some can just be incredibly hard to tear yourself away from and also have features built in which makes it feel like "Oh but just one more...." and a 3yo can't fight this and even less so if they have struggles with attention control, so it's not fair to expect them to. Games like that are not age appropriate even if they are rated 3+.
I agree it's hugely helpful to put boundaries in place early, before you feel resentful. If you notice that you are getting resentful, try to note down what you noticed about it afterwards because it will help you figure out patterns which will help with where to draw the line of where the boundary should be. I found Janet Lansbury incredibly helpful with this. Also, if his emotions are very intense, try not to rescue him from them. It can be really difficult to avoid sort of "picking up" their emotions when they are intense. Something I found helpful with this is an approach called Conscious Discipline. They have a website/social media or there is a social media guy Mr. Chazz who talks about the different tips in short videos. One tip is that taking three long slow deep breaths is grounding enough to shift you from the reactive/emotional state into more of a conscious and rational state, and if you take the deep breaths face to face with your child, they will often naturally mirror you and this is more successful than asking them to breathe when they are angry. There is also an amazing book called When Your Kids Push Your Buttons which I found extremely helpful, it's about 99p on kindle. And if you like the How To Talk books, there is an app which costs about £3 (it's the one by Mythic Owl) and you can escape to the bathroom and quickly look up on your phone what to say/do which also helps a lot.
A set of sand timers from amazon can be really helpful - you can use them to show the amount of time you'll be unavailable or the amount of time you want them to try something before asking for help etc.
For no nursery days when you don't have another parent around to tag team with, I found it helps to have different lists of activities I can choose from rather than have to think up activities from scratch and I divide them up based on the amount of input I need to put in - fully involved, partially involved (e.g. set up or available to help periodically) and not involved (e.g. I can just watch or be in the same room doing something else). Then try to do at least one activity involving me more when I have the energy to do it, so I can lean on the others where I can be a bit less directly involved more for the rest of the day. Dividing the day up into sections a bit like a nursery/school day can also help a lot especially if you include transition jobs like clearing the table together after eating etc.