Overlapping of Internship and First corporate job - Should I give them the intern certificate which has an overlapping end date?

I fully concur with the views of Mr.Kumar. As the said internship happened to be a part of academics in the final year, I don't think that a day's overlap that too because of onboarding from home due to the universal Covid-19 endemics only at the instance of the prospective employer can have any effect on the internship that got actually completed earlier or on the joining of the job that was virtual only.
Anyway, perceptions can differ. Therefore, the poster should not hide the fact. If any query is raised he can explain.
Youngsters should always bear in mind that employment is a critical phase in one's life. Honesty, integrity and reliability are the basic qualities expected of an ideal employee rather than efficiency that can be acquired by experience.

Hey
Sorry for late update.
They ignored my case and everything’s fine. Going to complete 1 year at this ferm in next month :)