This is bound to go poorly.
1.) Who determines what animal mental well-being is?
2.) How is this defined? Especially across species.
3.) Science has barely figured out that rats are ticklish and plants feel pain. How on earth do they know what an animal is thinking or feeling at any time in an objective manner?
Answers:
1.) Bureaucrats who don't own animals, don't know what animals are like, or operate purely off of decisions that make them feel good rather than do good.
2.) As loosely as possible, and never more than that.
3.) They don't and won't until animals can magically speak and become human.
This is the same issue with trying to make animal owners "pet parents" or "guardians". Legally, that makes your animal a ward of the State. The State then gets to decide what's best for the animal, not you. Your animal is no longer protected by the far more useful and freedom-preserving "special property" laws and can thus be confiscated at any time for any reason the State deems admissible.
I leave you with a quote:
“Listen, Peaches, trickery is what humans are all about," said the voice of Maurice. "They're so keen on tricking one another all the time that they elect governments to do it for them.”
― Terry Pratchett, The Amazing Maurice and His Educated Rodents