Everything you said in this post is wrong.
Female Loki can exist because she was taken from her timeline, which was
pruned and then escaped before suffering the same fate by travelling between nexus events. I explained it in the post you quoted but images are sometimes stronger than words:
(timestamped)
Was that an illusion? An hallucination? No. It's a flashback. So yes, there can be a female Loki without a multiverse. That's the basic premise of the series. Variants pop up, and get pruned with their bogus timelines, or integrated into the TVA. No multiverse thanks to the pruning.
The TVA didn't have a fake goal and the entire story nor the video was fake. The only fake parts were the Time Keepers' true identity, what happens to people who get pruned and the origin of the TVA workers. Their role was real: operate as the active force of He Who Remains (they believed it was the Time Keepers) in order to protect the main timeline by pruning others. The story is real: a multiversal war really happened, as narrated by He Who Remains ( in the last episode, and the unification of the timeline prevented it to ever happen again by destroying the multiverse.
timestamped
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Once I figured our timeline, all I had to do was manage the flow of time, and prevent further branches. Hence the TVA." From the lion's mouth.
At no point in the series is there a single mention or implication of "as long as a universe doesn't result in a creation of Kang it doesn't get pruned and can exist just fine". It doesn't even make sense with a basic understanding of the final episode, because of this:
There is only one timeline looping around itself, the main one, overseen by He Who Remains. If "a universe doesn't result in a creation of Kang it doesn't get pruned and can exist just fine", as you say, then you would see multiple (an infinity really) of those alternative timelines you describe branching all over the place. But you don't, because the TVA, whose role is real, prune it and maintain a single timeline. That's the whole point of the show.
After Sylvie kills He Who Remains, you see the timeline branching uncontrollably
resulting in a multiverse.