Oh OP sounds like an absolute battle.
Firstly: solidarity. I have absolutely been there. Middle child did not sleep. I remember at this age he needed to be rocked for two hours every night to get the first ‘stage’ of sleep. He was then up and down til 11pm, when we would get a longer stage. If I didn’t keep a diary I wouldn’t believe it. And I would think anyone was insane doing that!!! I went back to work when he was around 9 months, covered in bruises. I remember meeting with my boss on day 1 and explained the sleep issues, and that I couldn’t get any block of sleep, so I kept bumping into things and my body couldn’t heal. I spent a quite a few months accidentally falling asleep at work, and had to develop strategies for o keep myself awake. Then I got pregnant with number 3 and the next patch gets hazy.
Secondly: tips. This time of year is grim with a crawling baby. Do console yourself that as soon as your youngest can toddle a bit, life will get significantly easier. I used to joke that my poor sleeper was like having a dog. He needed to be walked twice a day, morning and afternoon. They will both enjoy puddle jumping - all over weather suits and wellies are a must. For now, take them to the playground. Like, every day. Take a towel to dry the seats and stick your youngest in the baby swing. Your older one might be able to push him; encourage ?her/him (sorry I’ve forgotten) to chat to youngest. Tell them it will help speech etc. It will give you a break. Take a cup of tea in a takeaway cup and take five minutes. In fact, try to develop habits where you constantly encourage your eldest to share their stories with the younger one. It will really give your ears a break and might help with their bond. You might find it works best when the youngest is strapped in (!)
At home, but still outside, get some paintbrushes and do water painting on the driveway. Send the eldest on a scavenger hunt and then show baby what they’ve found. Assuming your garden is safe; you can sit for five minutes and have a cup of T.
The more time you spend outside, the less time people are inside messing up the house. I used to go to playgroups, rhyme time at the library and play cafes all for this specific reason. With you going back to work there may not be so much on at the weekend, but it’s worth hunting for a few things which you can then rota in. We used to go to the library every week (board book for the baby), maybe there’s a local museum or place of interest? It can be a bit stressful hauling two around, but it will get easier the more you do it. It might be worth getting a NT membership if there’s one with a good playground?
At home toys at this combined age I found: cars - garages etc with whizzing cars around, and any small world play. It’s a bit hit and miss. Middle child was bashing so could not play alongside eldest. Youngest and eldest (who were your exact ages) did from this age, very nicely. Worth a shot but don’t beat yourself up if they don’t.
Inside, accept that the house will be messy. Totally agree it needs to be clean with a crawling baby, but there will be toys and some mess around. Do what you can in terms of one tub tidy at the end of the day so you can just pop it on the sofa so you can vacuum quickly. Cliche, but the eldest will enjoy polishing with you, and spraying surfaces etc. Clean the sink whilst they’re in the bath. I remember some nights sitting down feeling like I was eyeball to eyeball with the bloody massive jumperoo. Horribly depressing, but a lifesaver during the day!!! By the time your youngest is 16-8 months old, things will be a lot easier - sleep, weather, your eldest properly settled into school. If your finances allow, consider a cleaner even for two hours a week to help you ease your transition back to work?
Consider getting a vacuum robot - we bought a mop/vacuum which is brill for a quick whizz round. Scale down your meals so you are reducing the washing up, get a dishwasher if you can. Consider one outfit at weekends; end of Saturday you wash everyone’s clothes, and stick them in the tumble. Sunday morning you get dressed out of the tumble. It is actual genuis! Reduce changing the beds to every fortnight. And when you do, again do it first thing so you can hang it all day, then put the same sheets back on the bed. The eldest can help put their clothes away. It will help them burn some energy so a win win! (Whilst I’m at reducing - baths every other day is much better for children’s skin.)
And finally - accept that this time is awful. It’s awful for everyone, of varying degrees, but it will pass. Right now you need tlc, sympathy, and as many short cuts as humanly possible. Other posters are right; the lack of sleep is truly terrible and once this is sorted, things will seem sooooo much better. For us, when the non-sleeper started walking (13 mo) there was the first drastic improvement with sleep, 18 months and he was fine. For now, please talk to your GP and HV. The HV should be especially helpful with practical advice. There’s no shame in admitting it’s tough.
Keep going, and good luck with going back to work. It will be difficult, but the break from the kids, and interactions with adults, may also help you see things differently too. Make sure you book plenty of leave so you can make the transition as smooth as possible if you can.