This might seem controversial, but you can play chess, either lichess (open source) or chess.com (more popular).

I am not a browser gamer, but i played bonk.io for some time. Its a fun pvp platformer.

Additionally, you can also look for multiplayer indie games on itch. It does not have a lot of multiplayer browser games, but if the laptop is “really trashy”, then running games natively should be faster than running them in browser.