...but then what was the trans-warp we saw in the later series?
We could well argue that "transwarp" always means "better than current warp". Thus, when Starfleet adopted the technology tested on the Excelsior
, the next rainbow became the new transwarp. And since the Borg drive clearly is better than the TNG era warp, it's transwarp by definition.
...or rather, switch back, since the TNG-era warp scale was used on Enterprise...
Uh, no, it wasn't, not really. We never got any ENT references to "warp 10 is infinite speed", and we never got any specific references to which warp factor would match which speed.
Not that canon material would allow us to establish the TOS or TNG equations, respectively - both are pure fan material, not supported by the shows and sometimes grossly contradicted by them. But even if we assume that the TOS scale was v=c*wf^3 and the TNG scale was as portrayed in the TNG Tech Manual, all the evidence in ENT is equally compatible with both of those scales. After all, the scales do not differ much from each other on low warp factors, and Archer's ship only ever reached warp 5 plus a few decimals.
IMHO, the similarity of the two scales on the lower figures is a good clue as to what happened. Scientists in the ENT and TOS eras were only familiar with low warp factors, since their machines could do no better. And they thought that those followed a simple pattern where it was power-optimal to fly at warp factors that were the cubic root of the speed. It was an elegant equation, so it made for a good natural law.
Yet after TOS, ships became faster, and it was found that the optimal power curve didn't obey the cubic law at higher warp factors - indeed, any TOS warp factor past 5 no longer fell on a power minimum at all, and thus wasn't a "true" warp factor. The power curve shown in TNG was discovered to be the true one, at least up to the new warp 9.
Of course, in TNG, ships struggled to get past the new warp 9. So it would only be natural to assume that after TNG, ships got better and the scientists once again discovered that the warp curve behaved differently from what they expected at high speeds. There were new power minima there, so by the time of "All Good Things..." the engineers would once again believe in warp factors past nine but below infinite speed.