They somehow moved the late 23rd century Earth Spacedock before the end of the 24th century to another Star system to become the Fleet Museum.
Project a low level warp field around the target (aka, the station itself would be able to do that) to lower its inertial mass, then have several ships establish tractor beams on it and Warp it to the intended destination in another star system.
Alternatively, since most SF technology is modular, its possible the top end of the spacedock can be detached from the lower bit, and then both can be moved independently with other ships.
Ds9 was able to lower its inertial mass to nothing using a low level subspace field and use thrusters to move itself to the mouth of the Wormhole in under a day.
The spacedocks also have thrusters for maintaining their orbital position, and because a spacedock was fully operational (unlike the patched Ds9 from the opening of the series), it would likely be able to change its location in a given star system by itself much like Ds9 did.
Apart from that, its possible that later starbases were equipped with Warp capabilities so they can move themselves.
I don't know if the new spacedock in the 25th century in Earth's orbit (the one from Picard) has Warp capabilities... possibly not... but anything from late 25th century or early 26th century might.
Yeah... remember, though, that a Galaxy Class starship is 42 decks high and 700 meters long. Something that big could easily do the work of a space station!
Yes, but one of the reasons the Galaxy class was so big was presumably so it can be in deep space for long stretches of time and conduct exploration.
In fairness, a Galaxy class would likely be on the level of a mobile Outpost... but not a starbase (which is technically much larger).
It would definitely still be useful to act as a 'staging area' for smaller ships... but Starfleet should really give it an industrial replicator or several to be able to service other ships and create a self-sustaining environment.
