In addition to its extremely distressing condition that even prolonged treatment failed to cure, the cat also lacked a home (was being cared for at a rescue I think?). Taking into account all of its circumstances, it does seem that euthanasia was an appropriate welfare decision.
The vet was completely entitled to say "No, euthanasia isn't justified," if that was her professional opinion. But according to the article, she didn't make that judgement at all (and certainly didn't communicate it to the client). The reason she kept it alive was her own distress, not the cat's interests.
I do sympathise to some extent. I think it was really stressful being a vet during the pandemic. But she got things very wrong.
EDIT: The cat was being cared for by "someone who regularly rescued cats" rather than at a rescue as such. Still suggests a lack of a stable long-term home. An unofficial 'rescuer' does raise questions