how do I ensure Bitcoin core isn’t running when I go to copy the .dat files? I have been using qt and so I can “exit” it and I assume that closes it and stops it running but being new to Ubuntu I’m not sure.
If you exit Bitcoin Core (right mouse on the system tray icon), it gives a popup telling you to wait until it's done. Once the popup disappears, you're good to go.
Take note the way you exit Bitcoin Core doesn't matter (unless you use command
kill), using shortcut Alt+F4 or press "X" on Bitcoin Core window will also show the pop up.