2002 buick century back passenger floor only (the floor well only)
fills up with a quart to half gallon water when rains and is driven.
No other water evidence from windshield, door or windows or upholstry.

You check the seals on the doors? The back door seals on the top of the door frame slide down easy on these cars.

x2 on the door seals. Mine kept falling down until I had to keep them up with double sided tape. Also check to make sure your window is going up all the way, and seating in the door frame properly.

Ensure the window goes up in general. A few of the Christmas tree pop its in both my back door panels are broke. Signs that those windows were fixed by previous owner.

Most of mine in both back doors were either broken, or stripped and wouldn't stay in. Bad window regulators are a very common problem in the Century. My right rear window didn't work at all when I had my car out just before I bought it. Luckily they fixed it before I got it.

No, try finding a same year regal with at least 1 working window. Passenger side one is starting to scare me, but I should be safe cause my drivers switches are broke locking the others from any input. From the looks of it there was a design change on the motors. I did also notice these doors don't completely seal out water cause I found water in the front door speaker brackets 2 days after a rain storm. My last thought was lifting the back seat to see if it comes from the trunk area. There are little tabs to release the bottom cushion.