No conflict.
See USCIS May 23 Q&A(#2)
It depends on when your original 12-month OPT ends. If end before April 1, then you are legal presence till Oct 1, not to work (no need to worry about 90 day unemployment). If end after H1 timely file, get cap-gap annotated I-20 from your school and keep working (90 days unemployment continue to count if not working).
If COS not requested, email service center immediately so they will send you H1 I-94.
The bad news is that USCIS didn't honor what they told DSOs earlier about not enforcing unemployment limit. In this latest Q&A, that 90 days unemployment causing status violation will be enforced.