I'm afraid I don't really have much news to share about that. It requires a complete rewrite of session handling and the on-disk session format, and that's just something I haven't gotten around to finishing yet.
I've updated the related issue earlier this week though: https://github.com/qutebrowser/qutebrowser/issues/5359#issue...
FWIW, saving isn't the problem - restoring a tab's back/forward history from the saved file is.