If you have a matrix server, then yes the mautrix-imessage bridge has a docker container. Beeper itself you can’t really self host as it’s their matrix server you live on (I haven’t checked out the beeper-selfhosted git yet).
I’m pretty sure the playbook is just docker under the hood on a service user instead of your normal user. There’s a way to run the playbook with docker as well (memory is fuzzy on that).