Late 2013 iMac and Mac Pro life extension.

NEVER EVER install third party security apps unless you want Mac OS to become unstable and possibly damaged.

Both machines as you know are obsolete and are considered vintage by Apple meaning Apple does not supply parts for them.

You can use them anyway you want however when they don't access websites and/or are not able to run third party apps that means they are no longer useful and should be replaced and recycled.

Your 2013 iMac is nearing end of life. It's already obsolete.

You can continue to use it as you have, but you will continue to hit more and more limits online with old browsers.

There are no hardware fixes to change this. There is no supported way to cram in a newer OS than Catalina. Make sure you have installed all of the Catalina updates that are available. OS 10.15.7 is the last.

Don't install junk like anti-virus or cleaning apps. Not really needed. You might run a manual scan from time to time if you experience issues. Malwarebytes is great for that.

Some might suggest you install a Linux OS of some flavor and continue on with that.

Not a bad idea if you're a bit of a hobbyist.

Catalina, Big Sur, and Monterey are no longer among "the most recent three" – and are therefore unsupported, or soon to be unsupported, by the likes of Adobe and Microsoft.

They are enough to run current versions of Firefox, LibreOffice, the GNU Image Manipulation Program (GIMP), and the commercial Affinity V2 applications (Photo, Designer, Publisher). Those applications might let you extend the useful life of those old Macs a little longer.

FWIW, a Late 2013 iMac supports up to macOS Catalina, a 2013 Mac Pro up to Monterey. As noted, do not install third-party security software.

Just to add, if you actually meant a 2013 MacBook Pro, that supports up to macOS Big Sur.