First, they swabbed the whole deck not just the poop deck. The focus on the poopdeck is probably modern because it sounds interesting and sticks more in the mind.

Supposedly they swabbed the decks in part because salt water prevents wood rotting (versus fresh water from rain storms which promotes rotting), in part because it's a wooden ship with gunpowder loose which is a fire risk (so best to sweep it away and keep areas damp), and in part because it kept the crew occupied.

What is this assumption based on? Are there texts showing this or is it a Hollywood fact

Growing up I only remember ever heard it as "swab the deck". Calling out the poop deck specifically is likely a modern or regional inclusion because, well, "poop".

Or maybe it's one of those Mandela Effect things and I've left my original universe.

I'd wager that they wanted the entire deck stabbed swabbed, but with extra attention paid to the poop deck. That's where the important stuff happened.

We'll never know

What happens on the poopdeck stays in the poopdeck

Cuz that's where the poop is!