I’ve read that best practice is to do a database dump, in addition to backing up all the data files. It’s my understanding that there’s a slight chance of corrupting something in the database if you don’t stop the service first, since something could be changed while you’re doing your backup.
The easiest solution for me, as well as for being able to just restore my files and start the service again somewhere else, is to stop, backup, and restart. It’s down for less than 5 minutes while i’m asleep. If I expected better uptime than that I wouldn’t be trying to self host.