@Graylynne0
I'm very sorry to hear you had such a bad experience from your very first time hosting. No doubt you will get a lot of responses from hosts telling you that hosting long-term guests is complete madness. As a long-term host, I wanted to give you my perspective.
1. Firstly, the nay-sayers might be right. Are you aware of the laws regarding tenants' rights in your area? In many places, a guest that stays over a certain number of days (e.g. 28) obtains these rights and it's really not a simple process to evict them if they stop paying or are a big problem in another way. Therefore, do make sure you know your rights as a landlord (not just an Airbnb host) to avoid that situation. I know that is not your current problem, i.e. you had a guest leave early rather than overstay, but it's worth thinking about for the future, especially in regards to my next point.
2. Airbnb might take their own fees upfront, but they collect the accommodation payments from the guest monthly before transferring them to you. So, the booking goes ahead providing Airbnb can collect their that first payment. After that, a dishonest guest can simply cancel the payment method they used and Airbnb are unable to collect and will not cover you the host for that loss.
3. Why on earth are you discounting from £12,000 to $5,000? Is this based on Airbnb recommendations? If so, ignore them. I know it's tempting to offer low prices as a new host, but the Airbnb recommendations are nonsense. What are you basing your prices on? Have you researched the local competition? Have you worked out what you need to cover costs? Base your prices on what is both desirable but also reasonable. A low price/huge discounts may attract less than desirable guests, whereas an overblown starting price will disadvantage you in the search results. I offer a 10% weekly discount and a 15% monthly discount and I have a Strict policy. A Strict policy does not give guests discounts and, anyway, it's irrelevant because Airbnb's long-term policy overrides that and applies to any stays of 28 days or more.
4. DO NOT initiate the cancellation from your end as there are numerous penalties (including financial) when a host cancels. You need to get Airbnb to cancel this reservation for you penalty free. I know that getting help from customer services right now is a nightmare. They are understaffed since COVID cut backs and a lot of them seem poorly trained. Persist. You have evidence that the guest has left. If the guest is refusing to cancel, Airbnb should do it, not you.
5. In future, make sure you vet guests as best you can, especially long-term ones. Ask questions, check out reviews, require verified Govt ID, whatever you can and have very clearly stated house rules that the guests must acknowledge they accept in writing to you via the Airbnb messaging system. Although I use Instant Book, I would not recommend it for new hosts. Stick to request bookings for starters.
I wish you luck with getting your calendar unblocked and hope that you have a string of lovely guests from now on. My experience is that these nightmare guests come along once in a while, but are not the norm, otherwise I wouldn't still be doing this years down the line!