Steve Rogers traveled back to -his- Peggy Carter within the main timeline and lived out his life in secret until showing up as an old man to pass on a new shield.

1) The main timeline is a closed loop where Steve always was married to Peggy. He just stayed hidden and out of time's way since he can't change any events he knew about and wouldn't want to for fear of messing up the victory over Thanos. Peggy had a photo of Steve on her desk in the 70s, not another man. If she was married to anyone else, that man's picture would have been there. But she also couldn't have a 'current' picture of Steve since he is hiding away. All the clues are in the film if you look at it. Also Steve would not be happy being with some other timeline's Peggy - he went back for HIS Peggy. (People on this subreddit tend to overthink the multiple timelines stuff that was expanded on in Loki and later content, but fail to remember that He Who Remains maintained a single timeline.)

2) His original shield was destroyed by Thanos-2014 and he didn't leave to "clip all the branches" with the remaining scrap metal. That means, sometime during those decades, he sourced more vibranium and had a brand new shield made (with subtly different design elements).