People claiming that Loki is in an alternate TVA at the end

Probably it's a bit more complicated. Timelines and loops.

The TVA might be outside of the timeline but it's still influenced by timelines. So killing "He who remains" they reset the whole universe, not just that timeline. And that includes the TVA, it's start and evolution.

Remember the last scene? Instead of having statues of the 3 TimeKeepers we saw a statue of "He who remains" ... so thie TVA IS 100% different. Why did Loki get back to that version?? NO idea.

But the show doesn't try to stay very consistent anyway.

I could be wrong, but the show never really explained the TVA managing all timelines (universes). It was about sticking to the script of what that specific timeline was supposed to be, which is why they snatched Loki to begin with. He's supposed to die to Thanos in that specific timeline. His nexus event was grabbing the tessaract.

You could argue Sylvie and Loki being in the same TVA could go against that, but there's something weird about Sylvie. We know the nexus event of all the alternate-universe Lokis (Kid Loki killing Thor etc), but we don't know Sylvie's. So far it looks like they sent her to the TVA just for existing.

You could argue that a drawer full of infinity stones could go against it too. How did those stones get there if not from other universes? The show didn't explain.

For all we know, every Loki that Mobius was sent to correct resembled Tom Hiddleston, because that's that timeline's only Loki. Except for Sylvie who, again, is weird.

Now when it came to alternate-universal timeline Lokis converging into one area, it was in the Void. The Void is 100% outside all timelines and could be considered outside the TVA.

Then we get into The One Who Remains/Kang. He's outside them as well. And the show hinted that he's the guy who maintains the multiverse. So if he's the manager of the multiverse, then it makes sense the TVA is not, and that he created TVAs to handle their own timelines.

Ok, do people not pay attention at all? Where do you think all those different Lokis come from? A simple question.
Geez.. "THE timeline"... Really?

By now it's pretty clear that most of the stuff the TVA said about itself, timelines, and time at the beginning of the series, was a bunch of hooey.

This isn't Marvel setting up rules and then breaking them out of carelessness, this is both us and the Lokis finding out that the TVA orange thing was an "unreliable narrator".

My theory is that Kang wiped their memories and set up a statue of himself as the leader of the TVA.

Ok alienzen, that is a fantastic logical point. I agree with your summary - the TVA must itself exist outside the timeline of the universe for them to be able to determine what timeline is the sacred one and how to detect and chop off branches.