I always felt it was from the timeline that Steve spent with Peggy. Alot of people got the wrong idea that Steve spent his time in the current MCU timeline somehow staying on the downlow and not interfering with the world, however that would go against the logic of time travel that the movie itself setup. Any time travel is to a different version of the world you just left, otherwise time paradoxes would be possible.
Anyways, I believe that Steve didn't hide in this other timeline rather lived a fairly open life. He would have known that anything he did would not alter the original timeline so he could try his best to correct some of the errors in the past. Such as Bucky, Hydra and a few other loose threads he could do. Afterall he said himself. "If I see a situation pointed south, I can't ignore it. Sometimes I wish I could." He wouldn't have did nothing all that time.
As for the new shield, there a few things I can think of. It is the shield of that timeline. Either as-is or modified. Or he could have obtained Vibranium (either from Claw) or directly from Wakanda. Maybe he reached out to them earlier than in the normal MCU.
It is also possible that he had shrunk the pieces of his shield down and brought it with him to the past and had Howard Stark reforge the shield. After all he was the one to make the shield in the first place out of raw vibranium.
At the end of the day it was probably just something the writers wrote without putting as much thought into it. They wanted the shield destroyed like in the comics but also wanted to whole for Sam. So it was just there, no explanation given.
