I can’t grasp your use case I feel, pretty much all your complaints seem… odd. To me at least.
First subdomain. I think HA is completely right that proxy with a subpath is basically an anti-pattern that just makes things worse for you and is always a bad idea (with very few exceptions).
As for your tunnel I don’t know how you’ve set it up and I haven’t used tailscale but them only allowing one domain sounds like a very arbitrary limit, is it something that costs money to add? I use NetBird which I selfhost on my VPS and from there tunnel into my much beefier home setup.
Then docker in HAOS. The proper way I feel of running HA is for sure HAOS, and also running it in its own VM / or on dedicated hardware. This because you will likely need to couple additional hardware like a stick providing support for more protocols like ZigBee or Matter. It really isn’t a good solution for running all your self hosted stuff, and wasn’t ever intended to be. Running Plex in HA for instance is just a plain bad idea, even if it can be done. As such the need for an external drive seems strange as well. If you need to interact with storage you should set up a NAS and share over SAMBA. All this to say that HA should be one VM/Device, your docker environment another VM.
As for authentication there are 10k plus contributors to Home Assistant yearly but very few bother to make authentication more streamlined. I would’ve loved OpenID/OAuth2 support natively but there are ways to do so with custom components and in the end I quite strongly feel that if the end-users of your smarthome setup (i.e. the wife and kids) need to login to Home Assistant then you’ve probably got more work to do. Remote controls which interact with HA handle the vast majority of manual interaction and I’ve dabbled with self-hosted voice interfaces for the more complex operations.
Sorry if this came across as writing you on the nose, that’s not my intention. I just suspect you’re making things harder for yourself and maybe have a strange idea around how to selfhost in general?