There has been some confusion on why I say McConnell is "still in hospital" while his team claim he is 'discharged'

He was 'discharged' from the hospital's main medical care unit into 'Acute Rehab'

Unlike a normal rehab center (which the hospital has down the street) 'Acute Rehab' is a 16-bed rehab ward in the main hospital.

It has 24/7 nurses and doctors on site, and is reserved for patients under intense rehab who need constant medical supervision and support.

The attending physician says he is "not medically cleared to leave" that unit, and his Capitol Police unit remain outside the hospital main building where that is located (as we've seen in confirmations by @Cheering4Change)

These beds are critical to a hospital, and it's part of why they note it's for patients who can make reasonable recovery, 16-beds with 24/7 oversight.

1) You do not take up one of those beds for 3+ weeks if your issues are only mobility, even if you are a Senator with special treatment.