Mobile Application development

I am a coach and work with 8 different coaching platforms. 8 different calendars, respectively owned and managed by a different company. When client A books a slot with me on platform BetterUp for example, then the slot is taken on that platform. For 7 of the 8 platforms, it will update my Google Calendar and Apple Calendar, so I am fine seeing most of my meetings on one calendar. But what I can't do is update the other platforms and make my slot now taken. It will take a while for me to get to each one and cancel the slot. So I need some developed app to update these other slots automatically in real-time. This way it will avoid double bookings. Somehow the developed app can access each platform and do the job of updating. I can make all the platforms have the same exact slots I make all available for the same times. When taken, the other ones close up and can't be booked anymore.

Can you please help in building this kind of application and what would be estimated cost and time for the same