For databases, I usually host them on a separate server. This could either be through Docker Compose or a managed DB server. If a managed DB is affordable enough I'd reach for it.

It's because I like keeping my servers stateless when possible. It makes it easier to upgrade them in a zero downtime way later.

If your web server has your DB too, then you can't do zero downtime system upgrades. For example I would never upgrade Debian 12 to 13 on a live server. Instead, I'd make a new server with 13, get it all ready to go and tested and then when I'm ready flip over DNS or a floating IP address to the new server. This pattern works because both the old and new server can be writing to a database on a different server.

With all that said, if you were ok with 1 server, then yeah I'd for sure run it in Docker Compose.