For me it was Fallout 3. I played exclusively on console growing up but after seeing a video on YouTube about custom player homes I felt like I needed to give it a try.
Fallout 3 did allow the player to theme their house but if you really wanted to fully decorate it to have a lived in/cluttered look you had to drop items out of your inventory and make them kind of awkwardly hover in front of you. If you wanted to rotate them you'd have to carefully push it against something like a shelf until it was oriented how you liked it and hope you don't knock anything else over while placing it. Having things kind of welded in position or pre-placed was a big time saver.
The photo attached is from the Underground Hideout mod. It was one of the first mods I installed.
I'm wracking my brains trying to pinpoint the moment but it was so long ago it's a bit of a blur. If we don't count playing (and attempting to make) custom maps for StarCraft: Brood War or Counter-Strike I think it might have been for Diablo 2 back in the day. Though truth be told those were more like cheats if I recall - map packs with pre-revealed maps and the like. And I think there was an auto-loot?
Proper modding I think was installing early WeiDU mods for Baldur's Gate 2 back in what, 2004 or so? Would probably have been the old ease-of-use mod at the time plus stuff like romance tweaks, the "happy patch" and bonus merchants. Plus a ton of modded voice packs and portraits.