I had similar situation in Zurich with LX last year, late arrival, no hotel offered in transfer desk, because "everything is full", which was generally true, as there was indeed no available in apps of all popular hotel chains and only some shady private places left on booking.com.
Ended up calling hotels one by one and got a (last) room for 350 CHF in Novotel + 2x40 CHF for uber, Swiss offered 250 CHF + 2x40 CHF for uber and long email exchange did not change anything.
Eventually got back the remaining 100 CHF from revolut travel insurrance but whole experience was pathetic.