Water seeping through back passenger seat. What's the cause and fix? Chevy Impala?

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Check the rubber molding on the door the bottom edge. If that is gone that is how water gets into the car. Put down a dry newspaper over the spot and close the door then blast it with the water hose . If the newspaper is wet on the top then that is where your water is coming from.
Udder wise you are going to have to lift up the passenger seat and the backing so you can lift the carpet. Under the carpet is padding that acts like a sponge and that is why it is soaked. I use a pistol hair dryer and as the carpet is lifted up the hair dryer is positioned to point to the underlay and it is set to low and left on all night long. with windows mostly closed leaving just a small vent to let out the moisture. say 1/4" gap. Leave it running so it shoots toward the spot to dry it out and low is good for 8 hours. Now with the under lay dry and the carpet dry you can look under the underlay to see if you have a hole in the floor. Or expose the rear wheel well as tire splash can go through a tiny crack and make area wet. Figure out which it is and use roofing patch tar and paint it on inside the fenderwell or underside of the vehicle as the stuff stinks.(it works like UNDERCOATING) You can then reassemble the carpet and the seat. and you should be good.
. Otherwise a passenger dropped his bottle of water or alcohol or other like Pee and that is why it is wet.

Look at it logically FIRST. WHAT IS THE MOST LIKELIEST CAUSE...FROM WHERE? And go from there.

Only happens when you drive in rain? Go through rivers? Have windows down while it is raining. Have friends with leaky bladders? Partied so hearty you do not remember puking in the car?

One or two or 3 will be correct. Not bad out of 25 reasons for it to happen. IMO
Window weatherstriping is probably the least likeliest as that is the easiest to find, I mean, next to the whole in the glass or roof.

Maybe the easiest attack is just set up a pistol hair dryer on med/high so it shoots at the spot and leave it there for a couple of hours...to evaporate the moisture. The car is not 25 years old so perforation because of rust is least likely. I do not think Chevs had a problem with water leakage into the cabin....so part of the ride share is sharing in the spills.& mess.

Probable the rear window weather seal has been compromised. Look around the outside of your rear window and see if you can find a cracked rubber seal or rust nodules that have been broken open.

We can assume that your rider either spelt something or it's _ ee....
When you push into the seat more comes out because it's hasn't dried yet. There is foam in the seat and will work just like a sponge. (you compress it and the water comes out).

Maybe it leaked out of one of your customers.

I guess it must be leaking around the doors or the sunroof? Inspect it under actual rain conditions and with a light. Could be leaking around the fixed glass.

I think Earl would know this one. Earl? Come here Earl!