cookie clicker. i play it online online because i "play" it on the browser. perfect for second monitor and mindless. you don't have to deal with any people whatsoever.
you can also try old school runescape (that's actually online). it's basically the de facto second monitor game. there's lots of grindy stuff that is just relaxing to do, alongside good quests and hard challenges with regular content updates chosen by the community. im on a break though because i don't have a second monitor