I think the “wa” prefix means “bad” in Japan

There's a bit of a... pun(?) in there with its apparent origin as a name in Waluigi: The word is "waru" (noun) or "warui" (adjective), and with the "l" / "r" thing with Japanese pronunciation, "warui" and "luigi" combine really well.

Granted Wario was first in that franchise.

Correct. Another pun is that "ruigi" (類義) means "similar".