Adverb for particular kind of smile
He smiled soppily at his girlfriend.
soppy:
If you describe someone or something as soppy, you mean that they are foolishly sentimental. [British, informal]
He's constantly on the phone to his girlfriend being soppy.
She loves soppy love stories, old films, that sort of thing.
euphorically?
euphoric - characterized by or feeling intense excitement and happiness
enraptured [smile] - filled with great pleasure or joy
Edit to add sources:
euphoric is from: https://kathysteinemann.com/Musings/smiles/
'enrapture' - not sure. May have looked for synonyms of euphoric and it was just in search results.