Timekit should be able to do that. But if it’s not exactly what you’re looking for, you can try Checkfront, or eviivo. They have accommodation features.
Depending on what you’re syncing with Airbnb or Booking.com, you may need permission to use their API. If you’re just trying to link to the pages then you don’t need any third-party software. You would create a button that takes you to those respective pages.
But something like Checkfront or eviivo would be your best bet. Just Google “accommodation booking software”.