I have a wet carpet too. lifted the mat and it was soaked underneath
I haven't searched for the leak yet but I can almost guarantee it is the air con drip pipe which has fractured or a joint come apart.
It normally discharges through the bulkhead and drips outside.
I had an identical problem in a 2000 pathfinder.
It is not a leak from the screen, it hasn't rained in months. and it doesn't smell of coolant. just clean water. like you would get from an air con.
It's worse in the hot weather, when the air con is going flat out
Will let you know when I find it.