Parody, much like deconstruction, is used ad nauseam to describe things that do just enough to subvert the tropes of their genre to be slapped with the tag. One Punch Man uses Saitama's overpowered ability to tell a superhero story where the hero is just a bored slacker who's only obstacle is being taken seriously by significantly weaker, but more established heroes. It's not a parody of any particular character, but it cuts any tension that a battle shounen or Marvel/DC hero comic would build up for months on end by comically having the hero splatter super powered villains with a punch drawn on a single panel. I guess they say he was inspired by Anpanman but most of the people that say it's a parody of Anpanman hadn't seen an episode of Anpanman to make any connections genre-wise aside from the name and his outfit.
But I feel like the closest to accurate parody in recent anime has been directly poking fun at other properties like when Osomatsu-San made fun of Mad Max with a skit in the apocalypse where water is constantly hijacked or a race where a character is strapped to the bloodbag device from Fury Road, or the otome idol game parody with the brothers as androgynous pop idols that can solve world problems with bs magic, or even itself as they make fun of how the 60's and 80's versions of Osomatsu Kun were much more innocent times for the brothers and Iyami as they descend into debauchery and obscurity.
Or more direct parodies like Carnival Phantasm spoofing elements of Type Moon properties, or Gintama having characters dress up or act like other anime characters to make fun of their quirks in some situations.
Aside from obvious parodies, I feel like it's an overused term. Keijo is now a parody of sports manga by just having the sport be about fighting with women's assets, or Re:Zero is now a parody of light novels because the protagonist can be irredeemable at times. There's probably some garbage anime that people are saying is parody because it's incapable of doing anything right. Anything remotely different is now considered either satire, parody, or deconstruction even though it just does minor deviations that still ultimately play into the genre's cliches without having much fun ripping into any of the conventions people claim they mock.