I use screens shamelessly to get myself through days (not quite as bad) like this. Could you put on a dvd for them?
It depends on what your dc are safe doing. Perhaps a scavenger hunt in the park where you could sit on a bench and they have to look for items and bring them back. The rule is that you can’t move on to the next item until everyone finds what they need. That makes it cooperative rather than competitive (and automatically less noisy). I’m trying to think of games and activities that wear them out rather than you.
Hill rolling is ideal if you have a safe slope. You sit at the top and they roll down and run back up., we can get an hour out of that sometimes in our local park.
A great back garden activity is making a tinfoil river. Roll of tinfoil and a hose. Pinterest has loads of pictures, mostly with tots but it’s great with older kids too.
Sculpting with tinfoil might buy you half an hour or more and the clean up is easy. Anything with a sensory element tends to be a quieter activity I’ve found.
Would they go for something like sketching?
If they like lego try a big challenge like building a chair you can sit on. Or a tower that reaches the ceiling.
If they are used to the library it might be an option. Ours tends to have lots to do besides books. We follow a library trip with a “book lunch” where we read at the table. You can pick up a couple of dvds too for the evening.
Pop on an audio book or some podcasts to listen to. It will keep the noise down and everyone can be doing their own thing if cooperative play is beyond reach.
Or, if it’s an option for you, could you listen to a podcast or audio book or music on earphones? I do this at times to take the edge off and give myself a half break from the noise. I can still hear them obviously but it’s something else to focus on.
I hope something here helps or sparks an idea. Disturbed sleep is the worst.