Which processes systemd allows to live on after stopping an associated service depends on the kind of KillMode= (see systemd.kill(5)) that was specified for the service unit. The default ('control-group') is usually what you want, esp. if you are looking to not recreate the kind of chaos improper process management SysV-style init scripts frequently caused.

Chances are the k3s service unit specifies something else (like 'none') - whether or not that is actually wise would probably require some research.