There was an opera song playing in the background every time the 2 main couples were together.  It’s beautiful but painful too.
I was looking for it under the search for Love Affairs in the Afternoon OST and I couldn’t find it. It’s not in the track listing either (I have posted the listing in separate discussion).
So I typed the translation of the song (from the English subtitles) and voila I found it.
The song is called Le Secret, composed by Gabriel Urbain Fauré from Trois Mélodies (1879) Op. 23.

It’s about falling in love with someone. You want to shout your love from the rooftops, but you also want to keep it as this private, magical thing, just between the two of you.

After searching in YouTube I found that the version in the drama was sung by Barbara Bonney, accompanied by the Boston Symphony Orchestra, with Seiji Ozawa as the conductor. You can listen to it here https://youtu.be/h70KLit0a2o?si=p0Wo56PPUQOjmdw6

Le secret
French source: Armand Silvestre

Je veux que le matin l’ignore
Le nom que j’ai dit à la nuit,
Et qu’au vent de l’aube, sans bruit,
Comme une larme il s’évapore.

Je veux que le jour le proclame
L’amour qu’au matin j’ai caché,
Et, sur mon cœur ouvert penché,
Comme un grain d’encens il l’enflamme.

Je veux que le couchant l’oublie
Le secret que j’ai dit au jour
Et l’emporte, avec mon amour,
Aux plis de sa robe pâlie!


Lyrics (translated by Richard Stokes)

Would that the morn were unaware

Of the name I told to the night,


And that in the dawn breeze, silently,


It would vanish like a tear.

Would that the day might proclaim it,


The love I hid from the morn,


And poised above my open heart,


Like a grain of incense kindle it.

Would that the sunset might forget,


The secret I told to the day,


And would carry it and my love away


In the folds of its faded robe!