The TAS reference is not dated, nor associated with any particular species or culture; it could apply to an ancient discovery that resulted in the first AG technology known to the TAS-era UFP member species, some five thousand years before the UFP was even founded.
Earth's discovery of AG seems to predate Earth's discovery of alien cultures outside the Sol system, too: the interstellar abilities of the DY-100 were supposedly purely theoretical. Of course, the stasis box might have been found somewhere within Sol, perhaps even down on Earth rather than on the Moon where the 1968-92 time window would apply.
We know advanced AG tech was found down on Earth by Henry Starling in the 1960s, as per "Future's End". We never saw the tech applied by Starling, but for all we know, the AG systems on the Botany Bay
were manufactured by Starling's Chronowerx, and need not have been the first of their kind, even.
Starling's exploits were revealed to us through an 1990s vantage point. There weren't any hovercars in evidence in the 1980s, either, when ST4 showed us a corner of Earth. FWIW, both incidents showed us California - from our
vantage point, a likely location for practical applications of futuristic technology, either just for the heck of it or then for progressive environmental reasons. We might deduce that AG was confined to space applications at the time, then.
The main use might not have been to keep the astronauts' feet on the floor, though. Control of gravity would do more good if applied to propulsion issues: control of inertia would no doubt be closely related, and apparently was part of DY-100 technology as well, because the interiors showed no concessions to the application of forward thrust...
I find it rather plausible that Earth AG was indeed the doing of Starling and Chronowerx, and only saw spacecraft applications because Starling couldn't figure out how to reverse-engineer his captured spacecraft AG system to do anything else. However, AG is shown to be rather trivially available to every alien species, suggesting it's trivially easy to discover, too. Perhaps Khan and his super-friends were primarily created to do super-science, and invented AG for their respective patrons all across the globe roughly at the same time? Perhaps lesser, "ordinary" scientists did that, possibly back in the forties already?
But if the technology really was natively developed, I'd expect spinoffs and applications, and we see none in the 1960s, 80s and 90s visits to planet Earth. Or in the 2010s visit of "Past Tense", for that matter! Also, shipboard AG seems to be unreliable, limited or limiting in the 2030s still, as it's turned off aboard Ares IV in "One Small Step"... Then again, the propulsive prowess of that class of vessel (rescue mission was indicated to reach Mars from Earth in less than a week!) does suggest application of AG technology. All this in mind, I personally favor the idea of Starling peddling his poorly understood future tech for applications not much unlike DY-100.
Whether that future tech was Slaver in origin, we don't know - time loops are weird enough that the tech might not even have
an origin. But I'd like to think that the TAS discovery features into this somehow. Perhaps it being "the key" should be taken more literally than we have so far though? Perhaps the Slaver flying belt unlocked the mystery of Starling's AG technology?