People must surely still invent the occasional card game yet using a standard deck. It proves difficult for me to search this topic without running into a slew of new games using proprietary decks.
Also this isn’t meant to be about “house rules” situations within existing games although I suppose that is a likely way that games are invented.
How new do you want? Goofspiel is less than a century old; that’s the newest I can come up with off the top of my head. Egyptian Rat Screw might be newer; the Wikipedia article says merely that it’s based on a 19th-century game (but the older game is missing slapping, a key feature of ERS).
Regicide is a great game for 2-4 players (it may also play solo?) that has bobbed to the surface of popularity in the last couple of years, but as these rules say its best with two. Here are the rules - just note there are terms like “animal companions” or whatever, it’s just a name given to a standard playing card (in this case the “A”, or ace). Give it a try!
I remember Games Magazine (back when I had a subscription in the '80s and '90s) would have rules for new card games once in a blue moon. Specifically I remember liking a game called Parlement, although I think they mentioned that it was based on an older French game.
Tichu is relatively new to the USA, although it’s not strictly a standard deck (it has the 52 normal cards plus four more… you could make your own deck by buying two identical decks and writing on the jokers).
Barbu originated in the “early 20th century”. It’s a fantastic game for fairly serious trick-taking game players who have temporarily had their fill of Bridge, Hearts and Spades.
I was also going to mention games like Asshole or Screw Your Neighbor, usually drinking games. Asshole appears to be based on ancient East Asian “climbing” and “shedding” games, but from what I could find, didn’t show up in the West until the late 70s.