Acts 22:3 English Standard Version
“I am a Jew, born in Tarsus in Cilicia, but brought up in this city, educated at the feet of Gamaliel according to the strict manner of the law of our fathers, being zealous for God as all of you are this day.
Strong's Greek 3844: Gen: from; dat: beside, in the presence of; acc: alongside of.
Here "at the feet of" or "alongside of" a rabbi is an idiom, a metaphor for being formally trained by a rabbi. Note the preposition.
The idiom comes from the literal image.
Ellicott's Commentary for English Readers
(3) Brought up in this city at the feet of Gamaliel.--His education may have begun shortly after he became a child of the Law, at the age of twelve. (See Note on Luke 2:42.) He, too, had sat in the midst of the doctors, hearing and asking questions. The Rabbis sat in a high chair, and their scholars on the ground, and so they were literally at their master's feet.
The scene in Luke is different.
Luke 10:39 English Standard Version
And she had a sister called Mary, who sat at the Lord’s feet and listened to his teaching.
Strong's Greek 4314: To, towards, with. A strengthened form of pro; a preposition of direction; forward to, i.e. Toward.
In the case of Mary, the preposition is a different one. It indicates a location. Mary is not being formally trained by Jesus. She physically sat at the feet of Jesus.
These prepositions + accusative case are explained in https://ancientgreek.pressbooks.com/chapter/13/.
Is Luke applying the same meaning in Luke 10 as in Acts 22?
Yes, in the sense that both Mary and Paul were taught by their respective teachers.
No, in the sense of how formal was the training process. The verbs are different and the Greek prepositions are different. In Acts, the expression "educated alongside the feet of Gamaliel" is figurative. In Luke, "sat toward the feet of Jesus" is literal. Paul was formally trained as a Pharisee disciple by Gamaliel. Mary was informally taught as a disciple by Jesus.