Like all VPN-like things, some amount of data has to flow through their system. But almost everything is encrypted nowadays so it’s generally not too big of a worry.
For Tailscale though, they see way less. They see your IP during device setup, and maybe during use if things are making it hard for them to enable a direct connection. Depending on your DNS setup, they may see some of your DNS requests.
Its also really easy to setup your own headscale sever and then nothing goes to them at all. I recommend a small VPS for that, rather than running it on your home internet connection.