In particular, can the tmux session data be written to a file, and reloaded on reboot?
I'm thinking of something similar to Vim's
Assuming you could save the output of all panes to a file after the fact, you still have to restore the state of all processes in those panes. There was something like that at one point but it still has quite a few limitations. There is no such built-in functionality in tmux. This isn't like Vim which just has to remember which files you opened, whether you saved your work or not, where the cursor was, the history of inputs, etc.