Hi, I've cleaned the leaves and dirt from the same section in my car recently (just as a preventative maintenance and not due to any issues) and it did not look anywhere near as wet or moist as it does in your video, so as others have said there may be a blocked drain somewhere.
In relation to damp smell, I've had a similar issue in another car (not Audi) and what helped to get rid of it was one of those air con cleaners, which is a small canister that you put in the car and set off with AC/ventilation on full blast for about 10 minutes (it is like a mini smoke bomb). I was sceptical about it before, but in my case it sorted out the damp smell from the air con for good. That said, I don't think it was as bad as yours, as I was not experiencing damp seatbelts or windows fogging up. So you may well have other issues, but for the sake of less than £10 it may be worth a go (I think I bought the aircon cleaner for less than £5 a couple of years ago).