A hot restart can easily be triggered in Flutter on Linux by running:
kill -SIGUSR1 "$(pgrep -f flutter_tools.snapshot)"
on another pane or terminal.
It is then easily possible to bind this command to your favorite editor or IDE when changing the state of files.
There are of course extensions dedicated to this, but it can sometimes be interesting to know how to do this manually to improve your workflow.
Tested with Flutter 2.5.1 on Ubuntu 20.04