I would agree that it should be local organizations in the community on the ground. Local organizations know the individuals by name who need that support. It allows the support to happen fast and in a way that is timely for their situation.
I will highlight, exactly as you said, that this includes the municipal, provincial and federal governments.
Health care access is a huge part of our homelessness crisis. You hit it on the head. Local, clear and to-the-person connection is how that money will move fastest and have the most impact.