It’s definitely the membrane in the door by the sound of it – I had the same problem on a 2001 Passat, a 1986 Golf GTI, a 1990 Golf GTI, and a BMW E39 Touring. When you take the door trims off it’s actually quite difficult to believe that the bloody thing will leak so much into the car as it looks easier for the water to stay outside…
You need to carefully reseal the clear membrane all the way round. I did it with some black gungy gutter sealant stuff that never goes hard and then taped over with duck tape.
You’ll then need to either take out the sound proofing layer under the carpet to dry it out – or just wait for weeks before it dries out as the weather warms up (yeah right…)
NB, I never had any wet door cards or any other evidence at all other than the water in the footwell – took me ages to believe where the problem was coming from.
Oh, and I’d previously had the water from the bit under the battery coming through the rear hot air ducts so know all about that too. I love German cars, me, oh yes…