Why has the Time Variance Authority not intervened in the events of "What if...?"?

In order to understand the Sacred Timeline, you need to know about Kang the Conqueror and the Multiverse of Earth-199999, also known as the Marvel Cinematic Universe within the greater Marvel Multiverse. Note that there will be spoilers for Loki in this post, and especially episode 6. There is also a lot of this that was explained in writer interviews.

In the backstory for the MCU, there was in fact a multiverse, where every choice someone in the Earth-199999 universe made created a new timeline in this multiverse. Then, in the 31st century, an Earth scientist named Nathaniel Richards in each of these timelines discovered a way to travel between these universes. Many of the Richards were friendly, but there were also conquerors and tyrants, who wanted to conquer these new timelines and subjugate them. These variants are what's known as Kang the Conqueror, and they started the Multiversal War.

At one point, there was one variant of Nathaniel Richards, He Who Remains, who managed to control Alioth and used that power to take out all other variants of himself and establish a small group of timelines where Kang the Conqueror never existed and thus could never start the Multiversal War. This small group of timelines is called the Sacred Timeline, and it's that group what's the Time Variance Authority is protecting. So in effect, the TVA doesn't block ALL timelines from branching off from the Sacred Timeline, just those that would lead to Kang The Conqueror existing and starting a new Multiversal war. This was explained in a writer interview: https://screenrant.com/loki-show-kang-sacred-timeline-michael-waldron-response/

Now, there are 2 ways you could go from here to interpret how What-If fits into this system.

The first one is that these What-If scenarios are in fact just parallel timelines that the TVA doesn't see the need to prune, because they won't lead to an additional He Who Remains existing to start the Multiversal War. So in this context, the TVA won't intervene because it's still part of the Sacred Timeline.

The other interpretation is that after He Who Remains died, it collapsed the powers of the TVA to keep the Sacred Timeline pure across all of time and in effect allowed for timelines where Kang the Conqueror exists to split off from the Sacred Timeline. So now that the TVA no longer controls time and tries to keep the Sacred Timeline pure, these What-If scenarios are from these branched timelines that can once again appear all over the Sacred Timeline.

Loki shows Nexus events occurring in 1549, and when Loki was a child, which are both before the events of Captain America: The First Avenger.

Kang is at the "end of time", and his death allows branches to grow unpruned throughout the past.

The TVA is "for all time", not just for the future.

Loki Director Kate Herron has given some insight into this.

"So, there’s the branches, right, which is like the alternative reality. But then something, you’ll see it. It’s very subtle, but in the very last shot where you see the multiverse, there’s like basically other bigger physical timeline branches. So, it’s almost like these different separate trees that are now connecting."

It’s almost like a bridge. If you imagine the branch, it is like another reality. But if the branch extends beyond a certain point, it will then connect to other physical timelines. […] that last shot we did, there are other like thicker [branches] that are meant to be like our timeline. And there are other timelines like that and the branches are the connectors basically."

The Direct speculates as follows:

The multiverse is obviously something at the very heart of Marvel's Phase 4, and probably long after as well. One of those many branches is likely the one that will cause some problems for Spider-Man in the upcoming Spider-Man: No Way Home. And any number of branches will surely play a part in the madness that Doctor Strange's next film hints at.

Madness is also the best word to describe trying to understand the concept of timelines and alternate realities. It's a tough nut to crack, but there's no doubt Marvel President Kevin Feige and co. are hard at work making sure everything makes sense and is utilized in a meaningful way.

Fans will be taking a deep dive into the multiverse fairly soon, as Marvel's What If...? is set to premiere on Disney+ on August 11. The show will explore multiple alternate timelines where certain events in the MCU went much differently . The What If...? trailer even teases that some of those said timelines may interconnect at some point —much like the bridge that Kate Herron referenced.

The Time Variance Authority works to preserve The Sacred Timeline from branching, but there are other major timelines which do not intersect with The Sacred Timeline... until the events at the close of Loki and perhaps Doctor Strange in the Multiverse of Madness. This interpretation of the facts allows for the What If... timelines to exist without interference from the Time Variance Authority.