Pete Rose won't get in (and should not) because he bet on baseball.
And you think MLB is interested if determining if Ohtahni did ?
They would be if he wasn't a Dodger (or Yankee), and especially if he was an Astro.
Imagine everything was identical except the guy in question was Yordan Alvarez, you know MLB would leave no stone unturned and probably suspend him while he was under investigation because "they have to protect the integrity of baseball and democracy !"