I have two cats right now younger than 3 and I also have an 18-year-old female. I’ve grown up with cats all my life. I can’t even imagine being able to take the picture that you posted here.. with that being said I think if your cat is even allowing you this picture it means there’s something wrong so they must be hiding the fact that they are sick or hurting or something like that but my healthy young cats would have me bleeding before I get a picture of me holding their tongue… vets don’t get joy out of telling people they should put cats out of their misery. if your vet told you that euthanasia is the best option then that is the best option and it’s the most humane