I hope the title isn't a spoiler, I didn't feel like it was. Anyhow, after my final visit to the Institute, I realized I had not looted any of the Institute synth armor during the final quests, specifically the Institute Field Helmet which I badly wanted. The Institute is gone, is there anywhere I can still find armored synths or stashes of their armor?

Sometimes they attack. BOS checkpoints. Or i think they respawn back at the fort during the main quest

I guess I should have mentioned that the fort attack already occurred before I disabled the Institute in the final quest. I had hoped there would be corpses to loot but they vanished shortly after the battle.

Why would you want that armor? Looks like if pieces of a toilet were molded together to make armor, a porcelain man

it is

some of us don't even know, the institute exists

it's presented as a mystery in the first half of a game... something that nobody ever seen before

I'm genuinely sorry, I didn't think of that possibility, I'm usually an entire console behind everyone else to be honest. I like the helmet because it has sort of a Star Wars bounty hunter type look to it, not terribly keen on the body armor though.