Interesting observations. Some obvious consequences:

Hospital visitors and staff should never use patient toilets, ever.

Patients should use their own toilets only.

Staff gets clean scrubs after any visit to a toilet, helping a patient or on their own behalf. Yeah, sterile workers (surgery, etc) have to scrub in again after a bathroom break.

Clean patient bathrooms, including toilets, often, especially if infectious disease is present.

Design facilities to minimize the need to share bathrooms.

"Employees must wash hands before returning to work."

For what it's worth, hospitals already try to do this stuff.