If I open up a new tmux session,
/var/log/wtmp does not seem to get updated with the new session. This can be observed by setting up
watch "last -n 10" in one window, and then starting up a new tmux session in another. There’s no login getting logged, at least as far as
last can tell.
A little googling turned up https://bugs.launchpad.net/ubuntu/+source/tmux/+bug/1890406, which appears to be basically the same bug report but on Ubuntu. They suggest that this was a tmux bug fixed in a later version. However running with the latest tmux version (3.2a at the time of writing, also latest on nixpkgs-unstable) doesn’t fix the issue for me.