For some reason, it’s back to normal. Since around two days ago, my laptop can go into suspend mode again.
I think I figured out the cause of the problem
While this post suggests some peripherals to be responsible, I found that it was Steam that might be causing the problem
“Steam is currently blocking sleep and screen locking (Client interface)”
But now, the system can go into suspend mode regardless, even when the notification says that it is blocked. Or, by “sleep”, does it means the screen switching off? I’m not entirely sure. Weird. But I guess that’s Linux for you! I’ll take it any day