Owning pets is problematic in an ethical vegan framework. The industrial breeding of animals and the supporting industries are not compatible with many ethical thoughts on animal rights.
The problems you mentions follow from that.
Buying an animal inherently takes away it's innate agency and supports the animal breeding industry.
Feeding an animal vegan foods when it's natural diet would be from hunting is a side effect of buying an animal that you would have little chance of attracting from the wild.
When a breed is no longer capable of being a pet, you stop breeding it in captivity, and take care of all the of the living animals and manage the ethical quagmire that was completely manufactured.
Being vegan isn't a hard and fast set of rules. Adopting a pet from a shelter is sully supported by some and not by others.
Other who live with animals in cohabitation,opposed to ownership, could be fine for their way of life.