Yes you can actually self-host both Firefox sync server [1] and use Firefox accounts (which also can be self-hosted [2] and someone put something simpler in docker image [3]). And those can be used even with Firefox itself not only the forks.

[1] https://github.com/mozilla-services/syncstorage-rs

[2] https://mozilla.github.io/ecosystem-platform/tutorials/devel...

[3] https://github.com/jackyzy823/fxa-selfhosting