I think DS9 fits in with the rest of the TNG era depictions of starfleet's strength pretty well; in Emissary, the only ships capable of responding is the Enterprise (which just left), and a few Oberths that show up in the end FX shot. When Sisko goes missing, the Odyessy (which happened to be on it's way there anyway) is the only ship to respond. Even up to Way of the Warrior, when DS9 needed reinforcements, Starfleet could only send 6 ships that also showed up after most of the party was finished with. You don't start seeing large groups of Starfleet ships until the 'cold war' simmers for a while, and really kicks off in Call to Arms, even during the skirmishes with the Klingons.
You have to remember, that even with thousands of starships, the galaxy (or even just the part the Federation is operating in) is still a pretty big place, so even those thousands of ships are spread out to the point that when there's a big crisis without much warning, it's hard to get too many to the point of crisis in time to matter. But in the 6 months to a year the Federation had to gear up for the Dominion War, it's very likely that a great deal of the Starfleet that was off in the sticks got recalled and concentrated in the lead up to the fall of DS9, in addition to stepping up wartime construction of ships that could be ready and useful for the war to come, with other less useful projects being cancelled or put on hold (Lot of precedent for that; several battleship and large carrier projects got cancelled in the lead up to and the start of WWII by all powers involved, and likewise saw a lot of 'kitbash' conversions like the Independence CVLs, CVEs, and mass produced escorts).