The Harcourt Fenton Mudd I recall from TOS was not a formidable criminal much less a savage cold blooded killer.
"Harcourt Fenton Mudd. Thief –"
"Swindler and con man..."
"Liar and rogue."
"Did I leave you with that impression?"
– James T. Kirk and Harcourt Mudd, 2268 ("I, Mudd")
His TOS character was a thief, conman and a buffoon but not a Khan like character as seen in the last episode of Discovery. I only saw a brief scene but in it, he dispatched two lives in the most gruesome of ways, even going to far as to describe the death itself.
It's not a darker Mudd, it is a rewritten Mudd. So much so as to be a completely different character.