Should I Be Proactive or Just Keep Collecting the Paycheck?

I recently started a new J, but due to some internal delays, I currently have almost nothing to do.

At first, I was helping out with a few projects here and there, but lately I haven’t been assigned any work. There’s very little communication, and I’m still getting paid normally.

Would you stay completely quiet and enjoy the free paycheck, or occasionally send a message along the lines of, “I’m working on a few things at the moment. Let me know if there’s anything else I can help with”?

I’m wondering if showing some initiative could make me less likely to be let go if they eventually realize they don’t have enough work for me. On the other hand, maybe staying under the radar is the better move.