Two years ago, I was considering a Volkswagen Polo on Motability, partly because there’s a VW dealer just spitting-distance from home.
Even back then, there was a minimum 6-month wait for any VW. I phoned the VW garage and they confirmed the waiting time. It doesn’t surprise me at all that the wait time has increased and I fully expect that the waiting time for a WAV is even longer.
I found that wait completely unacceptable so I went with a different manufacturer (…part of the same group, supplying a car based on the ‘Polo’ but with a consideraby shorter lead-time).
Whoever told you that you could face a 3-month wait was probably basing that on info they had at the time. Any extended wait should be blamed on the actual manufacturer and an explanation demanded from them, rather than the motability agent themself !!
I would’ve hoped they could perhaps offer you a loan-vehicle while you wait ?