If you do not trust Tailscale as a company, here is an open source re-implementation of the server called headscale. Some/all clients are open source as well. So, you can review all components yourself or pay for a professional third-party review.
Otherwise, if you take a binary blob from any origin, including Tailscale, and have it run with privileges on your server, there are few limits on what this blob can do. Yes, backdoors are technically possible, but probably bad for Tailscale's business if that ever came to light.
I've always wanted to do this however do I understand it correctly that I need to host headscale on a vps server that is not in my tailnet/home network?
From what I understand tailscale is basically wire guard but made convenient. And how they do that is by managing you wire guard keys for you. So I would have assumed they could use the keys to access your network. HOWever while trying to look into this just now I found out tailnet lock exist and it says "When tailnet lock is enabled, even if Tailscale infrastructure is malicious or hacked, attackers can’t send or receive traffic on your tailnet."
If you're concerned about privacy I don't know why you'd use Tailscale over Wireguard directly. The latter is slightly more fiddly to configure, but you only do it once and there's no cloud middleman involved, just your devices talking directly to each other.
The official service is bound to need a SSO login from bad privacy related providers. They insist in not allowing a simple account creation with just email and password.
Not a response, but I used to use taikscale with my own headscale server without problems but for some reason it just started to fail (I didn't even updated tailscake nor headscake at all) and the speeds with direct connection were some unbelievable 0.00Mbps over direct connection.
I searched for another MeshVPN and I found something called NetMaker, you can Selfhosted it too and it works really well. The speed is better than Taikscale too because it uses kernel wireguard instead of user space. They still lack some features like an Android client but I don't care. I just want to connect servers securely. It's pretty new software so it can have some bugs.
The WireGuard encryptions stops when data reaches their servers and the data is re-encrypted to be sent to the client. So, theoretically, they can look at all the data being passed through.