Can "Book with Me" work with both M365 and Google Calendar integration in Outlook?

My company uses Microsoft 365 and I use Google Calendar. I've managed to connect my Google Calendar to Outlook so my colleagues can see any personal events show up as "Busy" on my work calendar.

My issue is that Outlook's 'Book with Me' feature doesn't seem to pick up my personal Google events, and allows bookings to occur over my personal events. Is this a bug? Can I somehow trigger Bookings to acknowledge these events?