What If...? makes it clear that in the MCU Prism of Endless Possibility™ (what some people call "the multiverse"), Infinity Stones from one universe work just fine in a bunch of other universes. Infinity Ultron doesn't just use them to attack the Watcher on his home turf — he uses them to punch the Watcher from one universe to another with merry abandon.
This does leave two other questions, which you may or may not actually be asking, but hey ho. (SPOILERS AHEAD!)
1. Where the heck is the Watcher? Is that a "dimension"?
As far as we can tell, "dimensions" in the MCU exist within universes — in What If...? episode 4, we see Doctor Strange in another universe confront and defeat Dormammu in his own universe's Dark Dimension. So wherever/whenever the Watcher is, it's presumably not a dimension.
It seems like he can observe and enter any universe he wants, so presumably he's outside of the universes, or something? But we don't yet have any description of where/when/how this place/realm/zone/whatever is — we just know that Infinity Ultron managed to access it, and the Watcher can host a cosy super-being mixer event there if required.
(In Doctor Strange and the Multiverse of Madness, we see the Gap Junction, described by Christine as the space between universes. Maybe that's where the Watcher hangs out? Is he friends with America Chavez?)
2. What's the deal with the TVA and the Infinity Stones?
As you say, in Loki, Infinity Stones apparently have no power in the TVA, as Loki's stolen Space Stone stops working there. We're later told that the TVA was created by He Who Remains, to maintain his victory in the multiversal war that raged between him and his variants, after he discovered and contacted them.
It's possible that during this apparently very long conflict, He Who Remains figured out a way to render Infinity Stones inert.
The TVA's capabilities to travel between and manipulate timelines and/or universes (which may or may not be the same thing) seem pretty extensive. If Tony Stark managed to build a machine that could destroy Infinity Stones — in a junkyard! In space! Out of SCRAP!!! — then in the apparently-very-long multiversal conflict that He Who Remains won, it's plausible he found a way to defend against the threat of one of his variants coming at him packing a Sparkly McGuffin or two.
It's possible that instead the TVA is merely located in a place or time where the Infinity Stones no longer have power, but we don't know when/where the TVA is either, and we haven't seen any other locations where Infinity Stones don't work.