I don’t know if he was happy. He just accepted what happened and made the most of it. He was still trying to follow the “rules” and knew there was no safe way to cross back over.
Also, in general, the Doctor is better at losing people… mostly because he has a lot of practice. How many people had he lost in his 900+ years (up until that point)? A lot. He has lost and learned to move on, but he never forgets. I don’t know if the doctor can ever be completely happy, not with everything he’s seen and experienced.
Just some thoughts!