Pointless random story; Mom asked if we could play Legend of Zelda together over the internet, said she wanted to try video games.
It took a while to get going, & to get our two sessions connected. Alas we could never get the various weird-workaround silly ways people had gotten controller-hand off to work. I should file a bug.
RetroArch is amazing. The do-all multi-tool of retro gaming. Well. Do almost-all.
I know this probably won’t help in your case, but if you both happen to have Nintendo Switches and have a Nintendo online subscription you get access to a bunch of NES and SNES games and can play them online together.
They even have a mode for people to watch and “clap” while one person plays a single player game.
It’s expensive to buy all that from scratch and closed to only the games that Nintendo has put on the service (Zelda is there I believe), however it “just works.”
On a handheld, I get to choose an emulation core for each game, most of them are too slow.
It would be good to have some idea which ones will actually work.