This is actually an interesting case. Openbsd implemented timing out the connection by adding it to the tty[1]. this sort of shenanigan would never fly on linux, "what! improve an unrelated established system, I don't think so." So for a long time doas on linux was not able to timeout a session. At some later point the timeout code was re-implemented on linux using a different mechanism[2].
If your linux doas does not timeout, try updating it?
If your linux doas does not timeout, try updating it?
1. http://man.openbsd.org/tty.4#TIOCSETVERAUTH
2. https://github.com/Duncaen/OpenDoas/blob/master/timestamp.c