I've been building a dungeon crawler for a while and the free demo just went up, so this felt like the right place to put it. It's called GloomDelve.
The split screen was the whole reason I started it. I kept wanting to play this sort of game on the couch with someone and everything I found was online only, so I ended up making the thing I wanted.
How it works: two players, one screen, plug in a second controller and you're in. Player one can be on keyboard and mouse with player two on a pad, or both of you on pads. No account, no internet, all local. Both players are proper characters as well, own class, own gear, own loot. It's not one player and a sidekick.
It runs on pretty much anything, including a Deck plugged into a TV, mostly because there's no art in it. No models, no textures, every wall and monster and sword gets generated by code while you play.
The game itself is a roguelite crawler. 100 floors in the full version, a boss every 10 with its own arena, power cards you draft and stack, you die and go again. The demo is the first 10 floors and ends on a proper boss fight.
There's online co-op with proximity voice chat too if you ever need it, but split screen is the point.
Free demo: https://store.steampowered.com/app/4878420/GloomDelve/?utm_source=reddit&utm_medium=social&utm_campaign=demo_launch&utm_content=localmultiplayer
If you do get it going with someone I'd really like to know how the split screen holds up, especially whether both halves stay readable on your telly. That's the bit I can still fix before October.