(Please tell me if his Study permit has expired and how many courses he is retaking this summer.)
Assuming that his Study Permit is still valid, he would list this last Winter semester as being a Student even though he withdrew. If he is re-taking course right now, he is still a Student/Studying, again assuming his Study Permit is still valid and he's taking 3 or more courses therefore a full-time student. Or, because it is the Summer, he can say that he is on summer break if he is not in school. If his Study Permit permits work (on or off campus) he can also say that he is Working during the summer. While on school breaks he can work full-time, but during school, he is only permitted to work 20hrs/wk.
If his Study Permit will expire soon, to be on the safe side given his past grades, I would apply for a renewed Study Permit AND also apply for an "OWP under TR to PR Pathway" for him (as your dependent/student on your TR to PR) which would be valid to the end of Dec 2024. It is possible that they might shorten the length of the Study Permit or refuse the Study Permit due to poor grades but it is up to the agents discretion. Given that this was his first semester, they would likely give him at least one or two semesters to recover his grades. If you also go for the "OWP under TR to PR", make sure his passport is up to date and does not expire before Dec 31, 2024 to maximize the length of the OWP validity. Many folks are not reading the fine print that says IRCC (generally) will not provide permits with an expiry date beyond the validity of their travel documents (usually a passport).
I hope you and your family get PR soon. Also, I recommend that he only takes 3 courses in the Fall if you have not yet received PR. He will still be a full-time student and have more time to focus on improving his grades.