Catalina

Your last macOS upgrade will be to High Sierra for that mid-2011 iMac — if you choose, and that means a useful iTunes, and Security/browser updates for another year. Your iMac is on Apple's U.S. Vintage list which means that no Apple Store, or Apple Authorized Service Provider will service it. You may find the lack of service when something goes wrong an untenable issue.

from A²…

If it runs the apps you need, I'd say it's not yet obsolete.

I would label Catalina an update, not an upgrade. It has some problems, so if I were you, I wouldn't feel bad about not being able to install it.