From my experience with tailscale so far - there are so many different ways to have it configured well. If it works well for you having it on the host, then go for it. I have home assistant in a VM with tailscale and tailscale on the (windows) host. This works well for my needs and I don’t mind having it running “twice”
I chose to set up grafana, mqtt, etc for an RV instead of home assistant. Little more lightweight for the raspberry pi 3 I used. Pulling together solar info, so we could see how long the AC would keep running on the road
I hope the homeassistant guys already have this covered, because I didn’t use it 4 years ago to know
I think I had a similar problem a couple weeks ago. Make sure they are adding the device to your tailnet, by default it adds the new machine to their own tailnet. I know I hit some kind of issue like that, at least.
Have you considered putting your children in one of the storage freezers? /s