Currently it is not possible to teleport to a private server when you are already in a game.
TeleportToPrivateServer only works with reserved servers.
I understand that it is possible for players to accomplish this by quitting the game, going to the Roblox home page and join from there.
However, as a dev I want to have a interface within the game that makes it seamless for players to join any other players in other servers, including the ones in private server (if they have the right permission)
To elaborate a bit more on how this is very frustrating, my game has both a normal lobby and a pro lobby.
If a player created and joined their own private server from the Roblox homepage, their friends can only join through the Roblox homepage.
But if the same player in their own private server teleport to the pro lobby (a different place in the same experience), their friends can only join them from inside the game.
This makes for very player hostile user experience.
a workaround for this is to do the opposite whenever a player joins a private server from home page, check game.PrivateServerOwnerId and teleport them to a reserved server created thru teleport service and store the access code in data store
now you can teleport other players to that server from an in-game interface
I want to express though that this workaround would make it impossible for other players to join the game from roblox home page, as the private server would be changed into a reserve server.
So I would still like to see Roblox give as a solution that allows players to join the player seamlessly from both private and reserve server either from the Roblox home page/screen or within the game