In my mind "filter" is some specific algorithm that does a single expected transformation

"Filter" is a Tik-tok / snapchat / instagram parlance for any kind of overlay / transformation. It's grown larger than just sepia filters and similar. All the ones that do facial tracking and overlay a mustache or w/e is funny in the moment are also referred to as filters.

See https://www.snapchat.com/lens

There's a pretty clear expected transformation here though? It takes an image and then reduces the "shiny-ness" of it by giving it the same transformation: change the sky to overcast, add material degradation like rust, reduce the landscaping by adding weeds/puddles, and remove the happy looking people.

Also adding random electrical infrastructure and random signs, also removing a statue in the distance in one of the images

Sure, that stuff too. The point still being that it's a pretty predictable set of changes being made to whatever photo you give it.

I'm pretty sure it's either gpt-image-1.5 or Nano Banana Pro in the background, with a prompt like "make it look worn down and slightly decaying".

Right, filtering is the reduction of information while diffusion/generation is creation.

It doesn't have to be a reduction. Swapping the colour channels would be a filter, but it's perfectly reversible.