How do I disable the screensaver on my MacBook Pro?

That's strange.

Let's try some other steps

If you have an M1 Mac, restart holding Shift to enter Safe Mode. Once loaded, restart normally and check again.

If you have an Intel Mac, do this

How to reset the SMC of your Mac - Apple Support

Reset NVRAM or PRAM on your Mac - Apple Support

Also boot in Safe Mode as I said before.

Check the situation again.

You can also test in another user. Go System Preferences > Users and Groups and add a new admin user.

Do not install anything there, just check if the screen saver behaves normally.

See this Use a screen saver on your Mac - Apple Support and uncheck "Show screen saver after..."