How do I stop double bookings?

Connect the iCal link from every platform you are still listed on. Each one exports a calendar URL; paste them all in. When a guest books on Airbnb, that date arrives here and closes on your direct site too, and the reverse happens when someone books direct.

Two habits close most of the remaining risk.

Add every platform, not just the busy one. A calendar you forgot is a calendar that will eventually sell a week you have already sold.

Block dates you are using yourself. Your own stays, a maintenance week, the fortnight your family visits — block them by hand so they behave exactly like a booking.

Now the part worth being honest about. iCal sync is not instant. It is a file that each platform publishes and we re-read periodically, so there is a window — usually minutes, occasionally longer if the other platform is slow — where a date is booked on one side and not yet closed on the other. Two guests booking the same night inside that same window is unlikely, but it is not impossible, and no iCal-based system anywhere avoids it.

If it happens, you will see both bookings here. Contact the guest you cannot host as early as you can and refund them in full.