The base spec for a HAF server is extremely small (something like 6GB of storage space).
So I suspect you're looking at the storage needs to store the entire blockchain (theoretically around 3.5TB, but in practice only around 1.2TB using zfs with lz4).
But like I said, the above storage space is only needed for a full API server that needs access to all the blockchain data. When you setup your HAF server for your HAF app, you just need to add a line to your hived config.ini file to filter out all but the operations you want. Then you'll have a super small database.
As far as docker goes, the recommended way to setup a HAF server is using docker nowadays. We're also creating a docker compose script for a setup of a full API node, but for setup of a simple HAF server, it all fits in one docker container, so no need for docker compose.
Does the database run in the same docker container? I will look again at the docs thank you!
The database software runs in the same container as hived (this is the "haf" docker), but by default you end up bind mounting your hived workdir and the database's storage to a local directory. If you use the script to create the docker it handles this process (command-line options to override defaults) or if you use the as-yet-unreleased docker compose script, you edit associated .env file.