@Fady14
Look for another management company. When I had a management company, they had a special portal where I could go to see the booking schedule, the rates they were charging the guest, the invoices to me, etc. I could add blocks to their calendar if I had booked anything on my own, or if I had friends staying. I couldn’t remove anything they had added, of course.
The only thing they didn’t do was sync to my calendar, but I got used to blocking their dates when I got a booking on my own.
There is a standard piece of software your management company can get to accomplish the above. I know it’s standard because I have seen the exact same Owner Portal interface on the sites of other management companies.