Firefox shouldn’t force you to restart and update like that unless something else, such as your package manager, has already replaced the executable files on your disk. In such a scenario Firefox doesn’t have any option except to inform you to restart it (well I guess it could choose to crash). But the mechanism that forced the update is the package manager.
Definitely does not work that way on my Windows 10 installation. When update is available, Firefox will have a “Restart to install updates” in menu button notification - but the files are not replaced on disk until you actually close (or restart) Firefox and thus Firefox continues to work normally.
What can happen though is that if you run another instance (ie. another profile) of Firefox while the first one has “staged” the update then that another instance can trigger the files to actually be replaced on disk but you would very deliberately do that.