Occam's razor is the simplest explanation, not the simplest statement.

Tautology has no explanatory power.

Incorrect explanations have less explanatory power.

This is true, but Occam's Razor is "the simplest explanation is usually correct", so we have an infinite regress.

Not if they've already been diagnosed with a mental illness, which is the situation at hand.

ok, so this is more like the Linda Problem. It is more likely that a person is a shitty person than a person is a shitty person and has a mental illness.

Hmm, there's an element you've left out of the situation that makes it different from a straight Linda Problem though. In logical terms, it looks like this.

  mental_illness -> shittiness
  being_a_naturally_shitty_person -> shittiness

And we know know two things: 1) the person in question is exhibiting shittiness 2) the person in question has been diagnosed with a mental illness. So:

  mental_illness = true
  shittiness = true

Whether being_a_naturally_shitty_person is true or false is something we have no information on.

So, from that starting point, we already have an account for the shittiness being exhibited since:

  mental_illness -> shittiness

  and

  mental_ilness = true

So if we want to go ahead and make the additional claim that being_a_naturally_shitty_person = true —you're violating Occam's Razor by introducing an unnecessary second cause when we already had a sufficient first one.