Did you ask the bird whether it wants to be nuked by you - or, by proxy, the vet - here? I don't call murder "euthanization" - that is just propaganda to sell to yourself that you have the right to decide who lives and who does not.
Right has nothing to do with it. It’s about power and responsibility.
It would be irresponsible to release parrot into an environment that is not its natural habitat.
Releasing it is just murder by neglect so people don't feel bad about themself that they actually killed their pet just because "they can't care" for it anymore aka they don't want to deal with the minor inconvenience of caring for a pet anymore. Or worse they become a pest that wipes out whole local ecosystems.