the federation will be around in the 4th millennium and is approaching Doctor Who levels of technological advancement.
You could maybe do a 25th century show and you could novels and comics set in later centuries fine but eventually it becomes hard to have a story when the tech is this advanced.
And yet, as you state, Doctor Who manages it. You could handle the technology issue in a couple of sentences: Previously unknown damage to the environment, too expensive, lack of resources, discovered to be unhealthy for prolonged use by humans, fallen out of fashion.