No need for Mozilla to make server software for this; Thunderbird/Lightning do CalDav and CardDav just fine, right? Seems that cs702's problem isn't with Thunderbird, it's with Google supporting CalDav and CardDav for sync.
If you want to self host, just host any CalDav or CardDav server software.
Thunderbird does not support carddav. Contacts + Thunderbird is generally a terrible experience. I switched to Zoho’s webmail because of this (at least I can get bidirectional sync to my iPhone).
If you want to self host, just host any CalDav or CardDav server software.