https://imgur.com/QlfvsS6.jpg I'm glad I listened to you.

Should I try to fasten it to any studs that I can find? Or is fastening it to the particle board enough?

First of all it's not a shitty basement room, it's going to be a home theatre/computer room. I mentioned it was a basement room to give full disclosure incase it mattered.

Nobody said to put silicone in drywall cracks. The previous owner filled the cracks between the particle board with silicone, taped over it, and then put a thin film of crackfill over that.

I was under the impression that walls had to have a fire resistant covering like drywall. I could very well be wrong though.

I also mentioned that I can't find any screws or nails, and I believe that they've glued the particle board to the studs. So if their intention was to maintain access to behind the studs then they're doing it wrong.

I've also never seen stucco used on interior walls in any house I've been in. It's always been drywalled.