Are you running the air conditioner? If the drain line is plugged, it will leak water (condensation) onto the passenger side floor.
My question, I didn't finish. Water intrusion into battery storage compartment in rear seat, which spreads to passenger side floor mats. Where's it coming from?
Water on the floor that is not coming from the heater core is coming either from rain water leaking around a windshield seal or one of the firewall seals where hoses, wires or other components enter from the engine compartment.
Your heater core is leaking. This is the part of your car that creates heat for the passenger compartment of your car. There is no fix for a leaking heater core except to replace it.
With a helper go to a car wash. Spray around the door and windshield with the helper inside to see where the water is coming from. This is the easiest way to find the leaks and plug or repair them.
If it is coming from the tank: NO. If it coming from the bowl: YES!
heater core may be leaking or hole in floor
Is it blood, oil, water, or urine?
There is a drain on the outside firewall that is clogged.
There is no drain hose for the refrigerant (134a) as this is a gas. There is a drain hose for water that is created by the evaporator and that is located on the passenger side of the engine compartment, near the floor boards. Unless it is plugged with debri such as leaves, water will drip there onto the ground.
you could have a heater core leaking or your windshield is leaking and the water is running down behind the dash and onto the floor.
bad heating core