Does headscale fully replace the corporate tailscale network? I've been looking at replacing my home wireguard if I can self-host tailscale but haven't had the free time to really figure out how much privacy I can retain by using headscale.

It definitely can. By default it ships with the normal Tailscale DERP map but it also ships with a default-off DERP server. You can turn that on and set your DERP map to only include that one server (or you can fan out a couple if you want). At that point you're not using Tailscale assets at all.

Thanks! Once I have some more time this winter I will take a look at using this to replace my wireguard setup.