The flatpak build avoids this problem by keeping both versions on the disk, up until you stop the app. Only at this time, the old version is removed, and the next start will be the new version.
This is the key point. I'm assuming that it downloads the update and then waits for me to agree to install it, but however it works it doesn't interrupt my browsing while I'm in the middle of something.
It's not an issue for these .deb packages because they enable the (experimental) forkserver.
You're mixing up two problems here. There's "please restart to update" that you can ignore/postpone, and there's "I have already updated and now going to sites is mostly broken" that you can't.
I hated the required restart with a passion when they first started it because restoring the previous session often failed. Once that worked, it was merely miserable (you still have to log in to all your sites).
Are you running very tight cookie/session settings or something? A restart definitely does not result in having to log in again for the stuff I'm logged in to.