port forwarding – SSH multiplexing hangs if it is not properly stopped

I am trying to configure remote access to my personal computer via SSH with multiplexing. Here is the configuration: from my laptop, I connect to a port on my modem; this port is forwarded to my router, which then forwards it to the local office and i authenticate myself with my key. Due to multiplexing, I can then open another connection to the home box without having to re-authenticate myself. It all works exactly as I expected.

However, a problem occurs when I restart the laptop. If I restart, I can no longer SSH in the startup box – trying to do so hangs a bit without asking me to authenticate, then expires.

I can fix the problem by restarting the welcome box (although this requires physical presence, which rather defeats the point). I can also avoid triggering the problem if I properly disconnect the SSH connection with ssh -O exit $IP -p $PORT.

Given the above, I have two questions: first, is this the expected behavior or have I encountered a bug? And, secondly, is there a way to avoid this problem? Thank you!

(This question is superficially similar to the configuration of the SSH multiplex timeout, but this The question concerns the restart / inaccessibility of the server while my question concerns the restart of the client without graciously signaling the end of the multiplexed connection.)