Have you launched Safari by holding the shift key to prevent it reloading its last application state? This would also be a good time to clear browser cache on the Develop menu, and clear all browser history. If you have any extensions loaded, I would uninstall them one at a time to see how the browser behaves on a relaunch. Also, ensure that of those extensions, that they are the most current updates.
Safari 14.1 is working just fine for me on macOS Mojave 10.14.6 and Big Sur 11.3. I purposely have no Catalina installed in the house.