Luigi Mangione

Depends. Particulars vary by state, but if such a claim was made then the court would likely order a psychological evaluation. In my state, if they determined that because of a mental illness he was not competent to stand trial or lacked capacity to appreciate the (legally) wrongful nature of his (alleged) actions at the time of the alleged crime, then either the charges might be dropped or he might be found Not Guilty by Reason of Insanity. In either case, that often (particularly for violent crimes) results in judicial commitment to a psychiatric hospital. Which can often result in a longer term of confinement than the prison sentence would have been.