@Hannah41 and @David126, so was it a booking request - that one is binding to the guest, you just click accept or decline, or was it just an inquiry, with perhaps Airbnb suggesting to pre approve ot to decline? Sounds to me like it was the latter.....and sounds to me like David responded to that.
So, If it was just an inquiry, not a booking request, and you pre-approved, the guest has the option to book or not to book. If you don't hear anything, then the guest didn't book with you. you cannot accept an inquiry and make it into a binding booking, you can only pre-approve.
the term "request" sure can be very confusing when used for all sorts of scenarios. I guess the term "booking request" clarifies that it is binding to the guest as soon as the host accepts.