I think the time travel of Endgame is very much like the time travel of Michael Crichton's Timeline, which was also based in ideas of quantum mechanics. You don't travel to your own universe's past, you travel to an identical parallel universe instead, to whatever year you choose because they all exist in all moments simultaneously and infinitely. Any changes you make continue to affect that universe, not yours. Ancient One talking about a branch was talking about only her universe getting fucked by losing the stones. They weren't dooming their own MCU by taking stones, but parallel universes. The Thanos that was fought and defeated was a parallel Thanos. The Loki that escaped was a parallel Loki. Tony had a nice conversation with a parallel Howard. Cap stood in the office and looked after a parallel Peggy. You get it.
Actually if I recall correctly, in the novel Timeline, when characters returned to their own time, there was no guarantee they had returned to their own original universe. But it's essentially identical, so nobody sweats it. It is assumed that parallels of the main characters returned to the main characters' universe, so it's not like they disappeared. Everything sort of falls into place and works out, like particles in an atom. Nobody is the wiser. It was, admittedly, a bit of a mindfuck for young me. But it works. Mindfuck-wise, it's like Star Trek, in a way, if you imagine that every time somebody transports, they are destroyed (killed) then a rebuilt copy emerges. But nobody cares, it's the same person, just move on.
Endgame actually provided an out for that issue, in the pad that they launch and return to. They always leave their own universe/time from that pad, and they always return to their own universe/time to the pad. The pad is the anchor to guarantee they get back to the "real" MCU. Otherwise, it's not really necessary, since the characters can travel through time and space on their own with only the suits, as Tony and Steve did. The only exception is Cap himself, who seems to have returned to his own past world and lived a life with Peggy without needing to arrive on the pad. But, consider that the timeline Cap returned to was again parallel. But it's identical, so he doesn't sweat it. Meanwhile, the Cap we see in the end, if he indeed lived a life with Peggy in the real MCU before strolling over to the bench, is actually a parallel Cap who did the same thing our Cap did. But he's identical, so nobody sweats it. It all falls into place like hadrons in atoms, or molecules in matter. Just roll with it.
