Похоже, что это часть именного составного глагольного сказуемого.

I've grown accustomed to her face.
She almost makes the day begin.
I've grown accustomed to the tune that
She whistles night and noon.
Her smiles, her frowns,
Her ups, her downs
Are second nature to me now;
Like breathing out and breathing in.
I was serenely independent and content before we met;
Surely I could always be that way again-
And yet
I've grown accustomed to her look;
Accustomed to her voice;
Accustomed to her face.

Это о возникшем чувстве, которое "проросло" в человеке.

Спасибо большое!🍫

🌷