I use LibreTube and it looks like half of the instances keep getting shut down and then get back up, and the speeds for all are atrociously slow that it is just better to watch it on YouTube on Firefox. I heard a while ago YouTube was blocking certain Piped instances but do not know if that is the same case right now.
I think the documentation by default doesn’t federate your instance so a private instance should be as accessible as your capabilities to get it up and running.