Well maybe not thousands but believe that a country as big as the federation would only have than a thousand or so ships is ridiculous because the. The Klingons would out numbered then pretty bad. Even though the Klingons are their allies it is never a good idea to show Klingons weakness.The exact line is " Twenty ships aren't enough to wage a war". That would still hold as a sensible statement if every major power had a total strength of several hundred, as opposed to many thousands.
(Picard explicitly refers to it as a fleet, even if it's not as large a one as he would have preferred.)
24 ships was all Picard had to work with. More would have come with time, for sure, but if you're saying we;'re meant to infer there were another thousand waiting just around the corner, that seems deeply unconvincing.
Ronald D Moore said he wouldn’t be suprised if starfleet had 30,000 because of the high registry. However since 3800 ships would practically lose the war for the federation then it’s probably or that big and since two elements of fleets (which could just be whole fleet since the 9th couldn’t make it) equals up to 627 (and no Klingon ships) and at least the 9th and the 3rd fleet weren’t there that’s not the whole darn fleet that they aleast have about 1,000. But they probably have more or else they would stand a chance against the dominion
So they would probably have 3,000 maybe and why we didn’t see it in TNG can be explained. Starfleet likes to mothball ships instead of retire them so they probably had a lot of ships in mothballs by TNG and got them out bu the war.