There's this really entertaining forensic psychiatrist named Eric Bender who does multiple analyses videos of pop culture "insane" characters using real scientific/medical knowledge.

• Here he talks about Ledger's Joker in Dark Knight. Summary = the Joker is psychopathic (violent, doesn't care about others, others are pawns for his "game"), but not psychotic (experiencing a break from reality, hearing voices, etc). Ledger's Joker would not qualify for an insanity defense because he knows what he's doing is "wrong" and experiences the real world as opposed to hallucinations. He's not mentally healthy or normal though and possibly doesn't understand how to interact with the world.
• Here he talks about Phoenix's Joker from "Joker". Summary = much the same as Ledger, but still interesting to watch. He discusses risk factors (abuse, neglect, genetics) that can be an extremely rare "Pathway to Violence" that could apply to the Joker in this movie.
• Here he talks about various Arkham Asylum inmates, including (briefly) various versions of the Joker. Summary = much the same, but also talks about Anti-Social Personality Disorder. Also, the fact Joker avoids capture means he knows what he's doing is "wrong" or at least illegal.

So the movie versions of Joker aren't insane in the sense that they're lost in hallucinations and unable to discern reality from make-believe. The Joker likely wouldn't be sent to an asylum in the real world. The Jokers of the movies are psychopathic, evil, uncaring, manipulative, etc. For the most part, to them the world is a game and it's all about the Joker being the main character with everyone else being pawns to be used for evil amusement.