As a side note on transporter capabilities in the (in-universe) future, the Expanded Universe novels (particularly, the "Department of Temporal Investigations" (DTI) sub-series, written by Christopher L. Bennett) elaborate on transporter technology in the 31st century of (what is implied to be) the "real" future timeline of the Federation.
The short story "The Collectors" (in DTI, C. L. Bennett) makes it fairly clear that 31st century Federation can beam living beings at least dozens of light years (a transport from Earth to Tandar Prime, a long-standing Federation member world about 40 LY from Earth, is specifically mentioned).
Note that all tie-in material is considered a lower class of canon than the series and movies. Ultimately, whether or not one considers these works a "real" part of the main on-screen continuity is mostly up to the reader.
Also, the Federation of the 29th century, seen on VOY:Relativity (Season 5 episode, fully canon), possesses "temporal transporters", which apparently function much like normal transporters, with the added ability to displace the traveler in time. The temporal range is never specified, but the spatial range is at least sufficient to reach from the Timeship Relativity's position (location unknown; 29th c.) to Voyager's position in the Delta Quadrant at the time, [note 1] and effectively simultaneously to Voyager's position in orbit of Mars when it was being built.
Unless the Relativity moved in its own time to cover the spatial distance between transports,  the effective spatial range of its temporal transporters is at least half the distance between Voyager and Earth in late VOY Season 5,  and more likely, the entire distance or more; call it 40,000+ LY. It is also possible the temporal transporter's range is not limited in space, at least not when also moving the traveler through time (see below).
It is unknown whether the spatial range of the the 29th century transporter is dependent on the temporal displacement.  However, the temporal transporters are never seen to move people through space (like regular transporters) without also moving them in time in the episode.
Bear in mind that the foregoing is (insofar as that is possible, an attempt at) an internally-consistent in-universe explanation. Out-of-universe, I have to agree with the Comments to the OP, e.g. this from user Tyson of the Northwest:
The limits of Transporters are "what won't break the story", the capabilities of transporters are "what is necessary to move the story"
Unfortunately for those of us who like logical structure, consistency, and plausibility, ST is mass-market space opera, and the aforementioned virtues were about as important to the creators as you'd think that would imply (which is to say, not very). I, for one, periodically need to remind myself that if that's what I want out of a story, I need to go read some hard SF again for a change. :)
It is true that the writers' bibles (mostly-binding creative guidelines) for the shows included some fairly concrete limits on what transporters can and can't do, but even those specs primarily saw technology (including but not limited to transporters) from an artistic viewpoint, as a narrative device, not from a scientific one.
- around the end of Season 5 - I'd have to do lengthy research to confirm, but off the top of my head, at that time they were perhaps 40,000 LY from Earth
- Unlikely - transports to the subjective past of the Delta Quadrant and Earth were made within what was implied to be a minimal interval in the Relativity's time frame. Given it is about 500 years ahead of the TNG era technologically, it is possible the Relativity can move across the galaxy in a short period of time; however, hopping around that way to carry out time-travel missions seems rather inconvenient.
- which would be the case if the Relativity specifically maneuvered into a position halfway between those points in its own time to minimize the spatial range its transporters need to cover - again, an unlikely inconvenience
- In plain English, whether it must move you in time to be able to move you in space; and, if so, whether there is some proportionality between the two - e.g. greater spatial displacement requiring a greater temporal displacement.