you're running multiple profiles of Firefox at the same time (so restarting one with a queued update writes the changes to disk, throwing the other profile instances out of alignment).
In that case, launching a different profile in a new window should not use the new version. In other words, Firefox should not do anything with the pending version until the user actually restarts the entire browser. Having the second window run in the new version just because there was a pending version seems like a bad approach.
The problem is that the user should not be prevented from browsing the web just because a new update is ready. The user should choose when to update. If the user has multiple important tabs open, they should be able to finish their work, but if Firefox refuses to load any new tabs, then the user cannot continue working normally.
I shared a screenshot, so I was not able to add text to the post. Maybe it’s possible, I don’t know. If there was a text box to add more text to the post, I would have explained the problem.
This is actually not unique to Nightly - the stable build does it, too.
I do recognize that scheduling updates is hard - no user ever wants to stop what they're doing and restart something, and it's important to keep users from running problematically out of date software.
I agree with OP though that this particular interaction is unusually frustrating for me. This message only appears after trying to load a link or a new tab, meaning it's actively waiting for me to want to use the browser before telling me that I can't, essentially guaranteeing it will interrupt my workflow.
I don't have a good suggestion on how to fix this without making the update system less robust - it might just be a necessary evil - but I do feel that OP's concern is legitimate.