There is no definitive answer here. I can only generalize about how we would handled it.
It is possible that we would have initially arrested him for being drunk in public. After a few hours he would have been released with no charges being filed. Our jurisdiction simply won't waste time going to court on drunk in public cases.
If he had gone back to the hotel, and had been arrested for trespassing, we would have cited him and told him not to go back. If he went back, we might have arrested him, and then the jail would have cited him right out again. And this could have happened several times. (Note here that our jurisdiction wouldn't have considered "trespassing" as something to incarcerate someone for a lengthy period of time without a court order.) Hopefully, at some point, and hopefully early, someone who had been told that he had mental health problems would have directed patrol or detention personnel to take him to the hospital and turned over to mental health personnel.
What was lacking in this case was compassion and common sense. And no amount of proper procedures training can be counted upon when common sense is lacking.
Am I correct in assuming you are a law enforcement officer?