Hello.
Yes, it’s possible.
You need to insert into one page the booking import shortcode for import from the Google Calendar and insert into other page the booking import shortcode for import bookings from booking.com
Watch this video guide about how to start import of .ics feeds (events/bookings) into Booking Calendar: https://wpbookingcalendar.com/help/import-ics-feed-video-tutorial/
Please note this info.
Booking Calendar plugin is supporting – import of events via .ics feeds from Google Calendar ( or Airbnb or any other calendar that support .ics format, like iCal application) – and export bookings to .ics feeds (files), which possible to import in Google Calendar (or Airbnb, Booking.com, HomeAway, TripAdvisor, VRBO, FlipKey and any other calendar that uses .ics format ).
Please read more about this feature here: https://wpbookingcalendar.com/faq/#sync
Please note, the import process is working in that case, when some visitor is open your website page with booking import shortcode. So you can configure CRON at your server, for periodically access this page with booking import shortcode to start import process. Or you can insert the import shortcode before booking form shortcode, so firstly system will start import process and only then show booking form, when someone visit your page.
Now about export. Booking Calendar is generate .ics feed with bookings in real time. But how often some service (like airbnb, or booking.com ) access this .ics feed to import the bookings from Booking Calendar into own system, does not depend from Booking Calendar. So in other words, Booking Calendar does not force to generate import process by third party service, when some booking is created. You need to check with support of this service (like airbnb or booking.com), about how often they can access the .ics feed tor making import.