Maybe in the UK, things were different. (Although again, Edge didn't pay it much mind, they instead spent their time on Galleon, "The next game from the creator of Tomb Raider!") Take-2 had better success with the franchise there (despite the creative energy to capture the feel of NYC/America, outside of the expansions,) maybe they concentrated exposure on 3 there. The world was on the web by 2001 though, and websites weren't going gaga for it either, most of their archives are up.
I'm telling you from experience though, maybe it was big on your playground, but I was in the business at the time (low on the totem pole; not claiming expertise, just saying I was around for all of these products and know how R*'s E3 booth loooked , and GTA3 was not the game everybody was running worldwide forecast predictions on.
I know GTA1/2 had radio stations, and GTA fans knew about that, but still, it was those types of features in GTA 3 which got it extended coverage in GameSpot and IGN (maybe partly because video was hard to download back then, but putting RealAudio track samplers up could help get around?) When they did a slew of little micro-features on stuff you could do or stuff you could find in the game, that's when it started to sink in that this game was way bigger than some "thug simulator".
The first two GTAs had their fans, but they couldn't convince people outside of those circles that they should spend some time with them. First one moved a million units worldwide, second game I'm not finding reports but maybe about the same (300k certified on PS1, not sure what other figures are out on GTA2.)
...Starting in August/September, before the game launched in October. The archive is still there:
https://www.ign.com/games/grand-theft-auto-iii/articles