There are several ports open (you dont open them, Tailscale does), including for peer relay. Some are vpn ports, but the ports for relay servers are not for VPN so my guess is that the software that listens to those ports is a lot less secure (compared to Wireguard or OpenVPN).
Yes my router has open ports, but it does not do any port forwarding. So I can 'directly' connect any device behind my router without my router needing to know any specifics of which device that is. And I don't need to do any port forwarding of anything on my network and thus expose them to the whole internet; I just expose them to the users of my tailscale network (only me)