Again we don't know that because the suit was not about patients, it was about workers at the facility. The court only rules on the case brought before them, not to make addendums on potential cases in the future. They are not going to rule "the mandate stands because of government funding, AND they can also force patients to be vaccinated." They only rule that the mandate is constitutional because the facilities do get government funding.
The bottom line is government has this control because of government money. How far that extends we will never know until the commies try to make another mandate for people receiving federal money.