You should display your temporary reference (not refinance) number until you receive your final registration number. I added it at the bottom of my description but you should also add it under policies and rules, regulations. You also need to include your EPC.
If you use other platforms to advertise your property, you need to show your number and EPC there too.
It's not really that you are letting Airbnb know, you are legally obliged to display this information anywhere you advertise, including in your property. This guidance is part of the information provided with your application and the council registration site.