This isn't just nagging. The API between the main browser context and content processes isn't stable between builds. This means that Firefox can't spin up a new content process if the update has replaced the executable with a different version. Therefore Firefox has the tough choice of trying anyways and risking misbehaviour (including possibly security bugs) or forcing the user to restart the browser process so that it can spawn new content processes.
It also depends on how your distribution updates Firefox. For most distributions they have this problem, however NixOS doesn't because the new version is installed in a new directory.
IIUC Firefox's self-updater also doesn't have this issue, and I think it supports Linux.