I submitted my i612 to USCIS and DS3035 at the same time ( receipt date Sep 2021- get the receipt number from USCIS and track my case status on DOS).
USCIS "case on hold" since Dec 2021.
i613 received on DOS on Jan 2022. (about 1 month).
my grace period ended Jan 14 2023.
I left to come back to home country on Jan 9 2023, arrived on Jan 11 2023. It showed Favor when I checked my status on Jan 12.
Now the university starts process my H1B application.