I know I'll get downvoted for this but I believe if you're vegan you really shouldn't have pets.
Having a pet means claiming total control over another sentient being's existence - deciding where they live, what they eat, their medical care, whether and with whom they can breed, and even when they die.
The usual justifications (they're happy, well-cared for, etc) still don't resolve the power imbalance. If keeping a human locked up from birth would be fucked up even if they were happy and loved you, then having that same level of control over an animal's life can't be ethical either.
The fact that we bred them to be dependent doesn't justify continuing a cycle of exploitation - it just highlights how deep the ethical problem goes.
PS. Caveat is injured wildlife that is being rehabilitated to be released back into the wild or animals that would find it literally impossible to survive on their own - ie end-of-life care or strays that will be euthanized - tho this means you should be actively dismantling the pet industry as well instead of just having pets but with an "ethical" undertone
I don't think vegans are out there buying pets from breeders. Or at least they shouldn't be.
We adopted two greyhounds from who were discarded from the racing industry. It's complex, because it sort of allows the industry to launder the hideous moral cost to be people that are not vegan but think dogs are special and cute. However even with the rehoming there are still mass graves full of greyhounds that were too old or slow that didn't get adopted, so it's not like forcing them to execute them would make the enormously profitable sport collapse.
It would be better if there were proper shelters and reserves for everyone and we stopped forced breeding programs but there aren't and the individuals seem to want to choose life over death.