A written exam is problematic if you want the students to demonstrate mastery of the the content of their own project. It's also problematic if the course is essentially about using tools well. Bringing those tools into the exam without letting in LLMs is very hard.

I don't entirely disagree but all exams are problematic. We don't have the technology to look into a person's mind and see what they know. An exam is an imperfect data point.

Ask the student to come to the exam and write something new, which is similar to what they've been working on at home but not the same. You can even let them bring what they've done at home for reference, which will help if they actually understand what they've produced to date.