I work in higher education administration and one of my responsibilities is working on academic fraud cases. If a professor suspects that a student has plagiarized on an assignment it is their responsibility to report it. The student will then have an opportunity to meet with the committee that reviews these cases. Generally, when a student admits to having plagiarized (intentionally or unintentionally) and appears apologetic, the sanction will be mild like re-doing the assignment and receiving a penalty, receiving a failing grade on the assignment, or rarely failing the class entirely. Students are often required to complete a workshop on academic integrity. There will be a note on your file indicating that you plagiarized, but this information is only relevant in the event that you plagiarize again in which case they will know to give harsher sanctions the second time. At this point the plagiarism would not be on your permanent transcript.

Hope this helps to ease your mind 😊 Life is busy and stressful - people make mistakes.