The TVA, or Time Variance Authority, was responsible for ensuring that timelines did not branch and that a single predetermined Timeline continued to run.
In other words, before its collapse, the entire storyline based on the Cinematic Universe had been unable to branch. Otherwise, it would have been "pruned" to prevent temporal tributaries from forming.
For example, Loki had come into contact with the Tesseract after the Battle of New York and successfully escaped. Such a variance had to be pruned, while that "Time Variant Loki" had to be brought to the TVA for trial, even "execution."
It was hard to say how far the TVA's jurisdiction extended, but so far, the world Harry knew differed only slightly from the Cinematic Universe's storyline. There was a high chance this universe also fell under the TVA's jurisdiction.
Then why had they not appeared to take him away?
That involved another phenomenon: if everyone in a certain place was destined to die, then no matter what timeline-branching actions they took, no branch would ultimately form.
Events that created timeline branches, such as "Loki accidentally obtained the Tesseract," were called Nexus Events by the TVA. A Loki like that was called a "Time Variant" or a "Time Criminal" and would be taken back to the TVA.
Yet that Loki had not been erased by the TVA. Instead, through a strange twist of fate, he had joined the TVA and hunted another clever Time Criminal.
That clever Time Criminal was also Loki. More precisely, she was a woman named Sylvie. She had found a way to hide within other timelines, making it impossible for the TVA to determine which world she had entered.
In the end, Variant Loki discovered the method she used to hide herself: any Nexus Event that occurred during an apocalypse