Syncing calendar with Bookings for a shared email account

Hi! I'm trying to create a booking system for a 1-user database. I used my institution's general email account, which is not associated with a particular staff member.

I created the shared Bookings page. I added the general email account to it as a staff member. I made myself unavailable for the Bookings page, so that all bookings will go to the general account.

However, I am not able to sync the manually added calendar events with Microsoft Bookings. In other words, if I manually add a booking to the general account's calendar, it doesn't show on Microsoft Bookings that the slot has been taken.

I believe the solution is to select 'Events on Office calendar affect availability' under Edit Staff. However, the option is greyed out.

I asked my institution's IT department, but they were unfamiliar with this. As it is a shared mail box, they don't think it has an admin.

My questions are, is it possible to sync a calendar with Bookings for a general account without an admin? If yes, how do you do it?

I hope this makes sense. Please let me know if anything is unclear and I will try to explain more. Thank you very much in advance for your help!