This is not something that is unique to the Home Assistant Tailscale add-on, but is the standard process by which a Tailscale node which has been configured to offer to other nodes the routing of packets to one or more subnets (i.e., to function as a Tailscale subnet router) gains the explicit approval of an administrator of one’s tailnet to publish that offer and to perform that routing.
In short, starting tailscaled with the option to have the applicable Tailscale node act as a subnet router (as in this case happens with the machine where Home Assistant runs) will not, absent “auto approver” configuration that is beyond the scope of this discussion, result in the node acting in the configured role unless and until an admin explicitly approves such.
A Tailscale exit node is effectively a subnet router that will route to anywhere on the Internet.