

Tailscale is a group of clients on a Tailnet which are all equal, unless you tell it otherwise. That means you need to set the client you installed on your router as a subnet router.
Even then, if you’re not familiar with networking, you’ll probably have duplicate routes if you’re not paying attention. The other option is to just install Tailscale on each server you want access to.
Yes, if Tailscale on your router is advertising routes, and your other devices while connected to Tailscale are picking up those advertised routes, they won’t be able to figure out how to get to your local network devices if both things are advertising the same routes.