Car on drivers seat on saturn sc1 3 door

classiic HVAC failure? LHD left hand drive car , no country told.
own for how long, 2years or 1day/ or what ( right passenger door?) for rain. ingress.
you said water, well that can be clean pure water
from RAIN or HVAC evap condensate,
using AC cool or heat + defrost mode? or just pure heat mode?
I do not know what you do there
i tray to capture water,in jar,and see if it is green or yellow or pink
that is AF antifreeze,
and put my fingers in it and rub fingers to thumb and it feels very very slippery, that is AF. not water
if i sniff it and smells sweet it is AF>
(3 ways to discover AF antifreeze)
ok it's water, so dont use AC or Defrost mode.
so that be RAIN or defrost condensart
sorry i could never even guess the water gravity effects from any car made from fire wall to rear of care, gee hills even change that.
learn to do deeper inspection of all carpets there.

bad door gasket
or last drove car with say a bandanna hanging out the door.
a 1 time event,nobody can guess ever.
and allowed rain to go inside any car.
or windows were not fully up.

Get your heater core checked. May be leaking.

If passenger side is dry it would point to a problem with the door seals on the drivers side either a door or sunroof if you have one. If there is that much water you could sit in the car, have someone use a garden hose or pressure washer on the door and sunroof to see where the leak comes from.

On a dry day take a garden hose and shoot water in any area that could leak and check and see if there is water in any of those areas. Also check under the car to see if there are holes or cracks that could leak. A rust spot will sometimes leak as well.

Dies car have a sunroof? If so, sunroof drain is clogged and backing up into car.

shop vac the carpet dry then spray garden hose around both rear doors or around doors and see if you get wet or see a leak. Also spray under vehicle on both sides of car and check for leak.

If you have a wet seat then it is likely defective weather stripping around the window.

Try this. If the floor is dry, then it rains and the floor remains dry, only gets wet after a drive in the rain or on wet streets, you may have a hole somewhere.

Check for holes from missing rubber grommets or holes in the floorboard or firewall from rust. Check for any rust holes or missing rubber grommets under the car or on the firewall, anywhere water can splash up into the vehicle from driving in rain or running through puddles..

Check wet spots along the carpeting all the way up under the dash, if the wet spot is higher than the floor itself, you could be getting the water from splashing through puddles.

Any holes under the car or in the fenderwell even up on the firewall can cause this problem.

First check for any obvious signs of rust, if none are found then look for missing or defective rubber grommets.

Is there a sweet smell inside the car?Heater core leak I beleive would be on passenger side floor.Antifreeze will be sweet to the nose.Are you getting any white smoke out the tailpipe? would likely be head gasket leak.Put a piece of cardboard under the car near the radiator and under the motor to see where its leaking from .One thing Ive learned over the years is that its going somewhere.On the ground? Or out the tailpipe.
As for the floor board leak the 98 s were prone to have the defrost area in front of windshield collect water from being plugged up .Mine was passenger floorboard.Daughter resealed small oval vent (that defrosts /heats hood?) LOL .Its on pass. side under hood on cowl .I think this will take care of my problem but you may need to investigate under the dash/defrost area and drill and then install a drain line to bottom of defroster.Exit drain line to O/Side of car...lol .Also was it raining ? was car outside in rain .if so it could be this issue.Sorry so long ,hope you can make heads or tails of this.

I believe the problem is a leak in your heater core. The water would run down the inside of the firewall or near it thus running under the mat.

Is it antifreeeze from heater core or heater core hose leak?  Is the leak pure water, or maybe something else?
Put it in the garage again overnight with an old white towel in the drivers foot well, best if you can find a way to stretch it from drivers seat forwar to firewall and keep it off of floor mat.  Check it before you go to bed,  then in the morning if no leak found yet.  see if the color/location of the spot helps you identify the source.  I think the heater core is under the dash center.  Anti freeze is green/yellow or orange.
good luck