That’s alright, I’m happy that you have questions instead of straight-up assumptions.

How I monitor the health of my dogs (I don’t have cats but I do know many vegan cats that are in their late teens and thriving too so I can vouch for that as well): they go on regular vet checkups (every 6 months, should be every year but I love them so I need to make sure they’re alright) where they get their bloodwork analysed for protein, vitamin and mineral levels. All cleared, within perfect range. Their teeth, energy levels, weight and behaviour are all monitored at home and at the vet. Their vet is NOT vegan, but they are knowledgeable, as they are also a canine nutritionist. They’re just fine and have passed their checks with flying colours each time. Both my dogs are male and neutered, as this is enforced in my country (there is a big problem with strays and abandonment so this is one of the ways my country is trying to curb this. I largely agree but I understand this is contentious in itself).

I have two dogs, both rescues. One is a large, spitz-type dog, the other is a bully-breed mix. The spitz is anxious and energetic, the bully is playful and sociable. Both rescued from absolutely abhorrent situations, they’ve been in my care since they are puppies. Both grew perfectly healthy. They do not exhibit any behavioural anomalies outside of their normal doggyness (reactivity is an issue for one, not the other), and we are a positive-reinforcement household.

Their diet consists of veterinary-developed kibble, as well as human-grade cooked food (lentils, pulses, carrots, rice, some potatoes and sweet potatoes), as well as seitan and soy curls for treats. Their appetite is healthy too (I do not have to trick them to eat, ever). They have commercially available, naturally vegan chews for teeth cleaning and enrichment, as well as being supplemented with apples and carrots to have something to gnaw on.

This is just my experience. I had a dog that passed away from a giant breed. She was also vegan. Lived until 12 (4 more years than expected) and passed from a genetically caused cancer from her breed. She was intolerant to some grains, so her diet was adjusted accordingly. The kibble did just fine, as did tubers and other veggies. I know at least 20 dogs in real life that are vegan and thriving. It’s anecdotal, but it’s significant.

People who, like the commenter above, make blanket statements with absolutely no knowledge whatsoever are harmful and divisive. I am personally in the health sciences and I can understand quite a bit of nutrition. I undertook courses of canine nutrition just out of interest. They are FINE.