(((Yours_Truly))), I am sorry you have to go through this experience. I think it's just awful to have to make this choice for a loved pet. Yet, when it comes to a vet advising this it's because it's the humane thing to do "for" that animal who is suffering and the quality of their life is poor and painful and the choice to euthanize is because the animal is going to die and the pain will get worse and death is inevitable.

We would prefer our pets die in their sleep in a peaceful way. When we euthanize that is what the veterinarian does, they heavily sedate them first and then they euthanize so it's not "painful" and the animal actually does pass in their sleep and the owner gets the chance to be there and love them.

Your cat has been so lucky to have a loving owner like you, always remember that. Animals who enjoy their life being loved by their owners are always so lucky as there are so many who don't have that happen for them.