@Alessio159 It can take a few days, a week, hopefully not more than that.
Yes, a host doesn't deal with refunds- the host doesn't get paid at all until 24 hours after a guest checks in. There have been many cases where a host who didn't understand the refund process refunded a guest, trying to be nice, only to have Airbnb also refund them, so the host not only didn't get the booking, they are out the $ twice.
I'm glad you got your money back and can stop stressing 🙂
And it's really refreshing to read a post by a guest who takes respoinsibility for not reading the cancellation policy thoroughly, as well as realizing that you should have communicated through the Airbnb messaging. (altho phone calls and texts are allowed after a confirmed reservation, they really should only be used for issues which aren't possibly contentious- like calling to tell a host you got lost, but you'll be there in 30 minutes) .
You wouldn't believe how many guests post here who are irate that they didn't get a full refund, and take zero responsibility for the fact that not only did they not read the cancellation policy, but they didn't even bother to read the listing description, then get upset because they can't bring their dog (when it clearly said no pets) or they assumed it was a whole private apartment, when it was listed as a private room in a shared home.
Guests like you who admit that they should have read something that they didn't, or paid more attention, instead of blaming others, are guests that people appreciate hosting. Hope you have some nice future bookings.