@Sisca0, Iwould send her a message via the airbnb thread to remind her of the checkout day and time and indicate that as by airbnb terms, overstaying costs the double normal rate. You have another guest arriving and need the room vacated at the hour agreed upon by the booking terms. (Repeat the checkout hour of the listing)
Suggest that she can easily find another place cheaper than “your double rate”.
And send a message / call airbnb as well to inform them a problem in that sense may arise, but you are working on it.
If you are thinking anout letting her stay on the couch, set up a shared room listing with strict house rules and a higher price.
I rent the same room as private room at 35 to 40 for longer stays, with normal rules, but when I’m in the apartment as well, I rent it as shared room at 43 (with breakfast), but they need to be out of the house between 10 am and 5 pm. A week maximum.
That works very well and gets repeat guests, both tourists and business travellers.
Personally, I would hesitate to let a clingy person stay, or someone searching for a home without really searching. I would offer the couch to a guest with a reasonable explanation why tgey have to stay a defined period longer. Never for free and only via a booking, if there was a tiny doubt.
Don’t forget to set a deposit, if you create a new listing.