Yes, you can reboot or disconnect the client all you want. tmux keeps your processes on the server safe, and you can ssh in and go back into your completely preserved tmux session.
Or are you randomly trying to connect tmux and Safari? Safari's update requirements are totally unrelated, but tmux can mitigate some of the problems they cause.
You're the one connecting tmux and Safari. My complaint is that a browser update should never require a reboot, especially for a browser that I never use.
I actually use screen on my laptop, but this is my workstation. It breaks rarely enough that also using screen on it doesn't make sense for me. But thanks for asking.
No updates besides kernel updates should require a reboot, yet here we are... Its pretty rare that I have to reboot my mac though, at least compared to my windows experience.
But above you said that you can’t reboot because you have too many ssh sessions open. Mkl’s suggestion of using tmux or screen would certainly help with solving the specific problem you mentioned preventing you from rebooting.
Or are you randomly trying to connect tmux and Safari? Safari's update requirements are totally unrelated, but tmux can mitigate some of the problems they cause.