Is it possible to upgrade my Big Sur 11.7.1 OS to Monterey?

then, sorry, no. Big Sur is as far as that iMac can go. it takes at least a late 2015 iMac to get Monterey.

I will add that if it still works for the things you need it for, there's no reason to stop using it.

we need to know the model and year of the Mac to let you know if you can upgrade to Monterey. it requires one of the Macs listed below: