Reinstalling the OS is a big deal and should be the last thing you do when you are troubleshooting a problem.
If your biggest problem is that Safari and Firefox browsers are misbehaving, it might be easiest to troubleshoot what is causing that rather than go scorched earth on the drive.
First - disable and uninstall any anti-virus apps, "clean up" or optimizing apps that you may have installed. These are very commonly the sources of trouble on the Mac, usually doing more damage than good. MacOS can take care of itself if you let it.
Protecting against malware in macOS - Apple Support:
https://support.apple.com/guide/security/protecting-against-malware-sec469d47bd8/1/web/1
XProtect Explained: How Your Mac’s Built-in Anti-malware Software Works - How-To Geek:
https://www.howtogeek.com/217043/xprotect-explained-how-your-macs-built-in-anti-malware-works/
Second - Have you tried restarting the Mac in Safe mode? (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.
How to use safe mode on your Mac - Apple Support
Safe mode disables loading third-party drivers, forces the OS to clear certain caches and logs and does other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.
Does the problem persist while in Safe mode?
Exit safe mode by restarting your Mac normally and re-evaluate the issue again.
Finally - I recommend that you run an EtreCheck evaluation of your Mac. EtreCheck is a diagnostic app that gathers important info about your hardware and software and reports it back to you. It is very highly regarded and meant to be used with Apple Support Communities to help others help you troubleshoot and resolve your Mac problems.
Please navigate to EtreCheck.com and download the free version of EtreCheck. Be sure to enable full disk access when you install the app. Once you’ve run the app and created your report please post it with your reply to this message.
You must upload the full report. To see how, please click > How to use Add Text when posting… EtreCheck Report.
We can use the EtreCheck report to look for the more obvious things that may be causing your problem and advise how to correct them.
EDIT - I, too, am currently using a mid-2012 MacBook Pro with Catalina 10.15.7 and it runs extremely well, including Safari and Firefox.
