Browser is Firefox 106.0.5 on KDE on Ubuntu 22.04.
I can’t reproduce this issue on my Firefox, Ubuntu too.
Do you have any add-ons to always show the url at the bottom?
I’m not sure what the issue is here. The browser can have any arbitrary piece of UI overlaid onto the web page, and it’s the browser’s job to make sure that they don’t obstruct content, not vice versa.
Besides, doesn’t the “browser message” move to the opposite side when your cursor goes close to it?