The general public was not aware that the Avengers had traveled to different timelines until Scott Lang, aka Ant-Man, revealed it in his memoir, Look Out For The Little Guy! which came out (in-universe) after the events of Spider-Man: Far From Home. This also means that the public doesn’t know that Captain America lived a long life with Peggy Carter in another timeline. (Scott tells his story of the Time Heist and the fight against Thanos in his book, but he keeps quiet about Captain America’s current situation.)
In his book, Scott shares his experience of being part of the Time Heist and other events in Avengers: Endgame. He explains in the book’s introductory chapter that he decided to write his memoir after getting encouragement from Bruce Banner (the Hulk) and Clint Barton (Hawkeye), who expressed their concern that the world didn’t really know what had happened and deserved to know the full story behind Thanos and the Blip, including their travels to alternate timelines. Scott writes:
One day, Bruce “the Hulk” Banner and Clint “Hawkeye” Barton took me out for lunch. They said they were concerned that the world didn’t really know what had happened with Thanos and the Blip and our long struggle to finally put things right again.
At first, as I usually do when confronted with heavy topics, I made a joke: “I’m pretty sure at least half the world knows what happened.”
Bruce responded that yes, of course, billions had experienced these jarring and mind-bending events, but they didn’t know the full story behind them. And ultimately, that’s what people need the most to get through and get past traumatic events: a narrative that helps it all make sense.
Before Scott Lang’s book came out (in-universe), Jennifer Walters, the protagonist of She-Hulk: Attorney at Law, was unaware of the details behind the Time Heist and assumed that Steve Rogers had died. She mentions this several times in the first episode, “A Normal Amount of Rage”. She refers to Steve using the past tense “was”, reflecting the common belief that he was among the fallen heroes.
However, Bruce Banner, who is Steve’s friend and fellow Avenger, knows that Steve is still alive as an old man. He uses the present tense “is” when talking about Steve with Jennifer, hinting at his secret survival.
Here are dialogue from the first episode, where Jennifer and Bruce discuss Steve Rogers (note the contrast between Jennifer’s and Bruce’s use of “was/is”) (emphasis mine):
Jennifer: Obviously, Captain America was a virgin.
Jennifer: [Drunk crying] It's just so sad. Steve Rogers did so much for his country and he never got to experience sex.
[Crying] Did you see that ass? Like, that ass did not [Cries] deserve to die a virgin. It's, like, so sad.
Bruce: Steve Rogers is not a virgin. He lost his virginity to a girl in 1943 on the USO tour.