Is my cat wild?

I fully agree with your examples. Our (individual) regular feeder visitors, despite knowing our homes are a source of food, aren’t reproduced, dispersed, or restrained by us. They can go wherever they please, and even if they eat out your hand, we’re not breeding Black-Capped Chickadees as we do our pet chickens, supplanting them in areas like we do freshwater sport fish, or restraining them like we do a zoo animal.
Mammal sanctuaries and parks would also fall under this provided the animals aren’t kept in some large fenced-in area, and similarly for those feral cats that don’t have owners.