Yes correct
If you don't trust tailscale then you can use headscale
Head great things about that havent tried it tho
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Headscale has some limits around ACL functionality that the tailscale coordinator has, and obviously doesn't have a flashy full-featured admin interface, but it more than gets the job done for a small user network. Mine's been going for at least a few years.
Tailscale alone is pretty safe. They'll know your device & network layout, and how much traffic each uses, but nothing more granular than that. Technically, you can do a lot with it running from a home server & on your phone on the go.