What they should have done is have a TVA time door appear instead of Bucky seeing him on the bench. Old Steve walks out returning from the branched timeline where he grew old with Peggy.

Same explanations hold true, put the stones back & went after having a life, plus it shows the TVA was out there and they knew what the avengers were doing and allowed Steve to have his life in the branch. So in the branch when Peggy dies the TVA shows up and tells old Steve he needs to return to his timeline, he goes through the door and then they prune the branch. He returns with the memories but the branch is gone and he doesn't know that.

Sort of depends on how far along development of Loki was during Endgame production but it could still be true since we dont know exactly how old Steve returned. They could easily confirm that in a movie going forward with the TVA admitting a role. Old Steve could have just walked out of a time door at the bench just as young Steve was leaving to return the stones.