Two low sleep needs kids here so you have my utmost sympathy regarding the sleep deprivation/late nights/broken nights/early mornings!
Average sleep needs for a 5 year old start at just 10hrs in total per 24hrs and as little as 8hrs is considered low, but still quite normal - for a 3 year old these figures are 11hrs and 9hrs respectively. So if you're putting them to bed before 8pm then a low sleep a needs five year old may genuinely have had enough sleep by 4am and the three year old by 5am, that 8/9hrs may actually be all they need.
We eat early with the kids (in practice, this means that on weekdays I eat early with the kids and my husband eats alone when he gets home - we sort of accepted that family meal times aren't possible currently) and then do as much clearing up as possible before bath time so there's less to do once they're down. We also each sit with one while they go to sleep so we get some of the nice one-to-one time (I especially value this now that the older one is a bit older as she often shares her worries and things at this time) and I think having that time sitting together listening to a kids' sleep meditation fills up their connection cups a bit so they're easier the next day. My husband often falls asleep during this bit! He does the overnights/early mornings and has the weekend lie ins (he's asleep now). We used to do it the other way round, whatever works for everyone to get sufficient sleep to be functional.
I also get every overwhelmed by the constant noise/barrage of talking. I will often say, "Mummy needs five minutes with no talking" and put a timer on Alexa (they accept timings much better from the tech than from us). Loop earphones are a lifesaver for toning it down a bit. As others have said you don't have to answer every question, you can just give a running commentary on what you're doing a lot of the time.
Do you have one of those small trampolines? Having one indoors was amazing at that stage where they clambered on everything. During school holidays we do breakfast, clearing up, get washed and dressed and go OUT, then their behaviour is much easier to manage in the afternoons. Sometimes I struggle to get us out in the morning and then regret it later on in the day...
It is absolutely relentless at that age but it goes get easier, ours are early/mid-primary age now and I do monthly cocktails with some other school mums, I'm in a book club, I go to the gym. Do you have a sense of a single change you could make that would really help you - weekly walk alone for half an hour, nap on Sunday afternoons, fortnightly phonecall with your best friend? It does get MUCH easier but I appreciate that does not help in the moment!