It's hard to recommend games when you don't have a baseline taste. The past couple of years having a demo became very common on Steam, so I suggest trying some demos.

You've played a 2D platformer and a multiplayer shooter, two very popular genres with massive offerings. If you're interested in more along the same lines, just off the top of my head I'll say try Hollow Knight as a 2D platformer, and Overwatch 2 as a multiplayer shooter (this one is free). Overwatch 2 may be overwhelming for someone new to gaming.

There is a genre called cozy games for more relaxed experiences, like Journey. There are also turn-based roguelikes, and for those I would recommend Balatro.

I don't know about Ubuntu or Linux compatbility so look into that, but I know Steam's OS and Proton have made massive strides.