Docker will let you run as many database containers as you want and route things such that each service only sees its own database and none of the others, plus even processes on your host machine can't connect unless you've configured ports for that.

Flatpaks are similar, but more aimed at desktop applications. Docker containers are made for services and give more isolation on the network.

Docker containers get their own IP addresses, they can discover each other internally, you get port forwarding, etc. Additionally you get volume mounts for persistent storage and other features.

Docker compose allows you to bring up multiple dependent containers as a group and manage connections between them, with persistent volumes. It'll handle lifecycle issues (restarting crashed containers) and health checks.

An example - say you want a Nextcloud service and an immich service running on the same host. You can create two docker-compose files that launch both of them, each with its own supporting database, and give each db and application persistent volumes for storage. Your applications can be exposed to the network and the databases only internally to other containers. You don't need to worry about port conflicts internally since each container is getting its own IP address. So those two MySQL DBs won't conflict with each other. All you need to do is ensure that publicly available services have a unique port forwarded to them. So less to keep track of.