In an essay "How I Came to the Cologne Carmel"* she describes the events leading up to her actual entrance into Carmel. However she doesn't say a lot about her interior experience. I don't know if there are other places in her writings where she goes into it more. But this is what she says:
"For almost 12 years, Carmel had been my goal; since summer 1921, when the Life of our Holy Mother Teresa had happened to fall into my hands and had put an end to my long search for the true Faith."
Then she narrates the external difficulties that prevented her from entering earlier. A lot of it had to do with not wanting to make things too painful for her ailing and elderly mother. It was hard enough for Frau Stein to accept that her daughter became a Catholic. For her, to see Edith enter Carmel was a great suffering.
Finally Edith felt God moving her to take the step. She narrates the painful talk with her mother. Edith reflected on the tearful scene as she rode on the train: "I could not feel any wild joy. The scene I had just left behind was too terrible for that. But I felt a deep peace, in the harbor of the divine will." Finally she arrived at the door of Carmel. "At last it opened, and in deep peace I crossed the threshold into the House of the Lord."
Her vocation to the religious life seems to have been born at the same time as her conversion to the Catholic faith. She simply states it had been her goal. Yet she also makes clear that she believed this was God's will for her.
It doesn't seem that she had any thought of entering the religious life simply because it was difficult, or because she thought it was a higher calling. She entered out of love for God, a search for the truth, and the desire to be deeply united to God by doing his will.
In his homily for her canonization, Pope John Paul said:
Aware of what her Jewish origins implied, Edith Stein spoke eloquently about them: “Beneath the Cross I understood the destiny of God’s People.... Indeed, today I know far better what it means to be the Lord’s bride under the sign of the Cross. But since it is a mystery, it can never be understood by reason alone.”
So it seems that Saint Edith Stein can especially shed light on the religious life insofar as it means being the bride of Christ standing at the foot of the Cross. This certainly has a Marian connection, for Mary actually stood there and saw Jesus die.
Mary, our Mother, Teacher, and Queen, obtain for us the grace to understand and better live the vocation God has called us to, just as you lived yours.
* In Edith Stein: Selected Writings, Springfield, IL: Templegate Publishers, 1990.