You asked the right question.

Let's start with a pretty universal basic.
A garbage bag wrapped around you is 100% waterproof right? Same with rubber boots. But the reason they are bad is because your body's moisture can't escape.

A wet body feels gross, but it's also bad because it's conductive. You lose heat at something like 10-30x the normal pace when the body is wet.

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You are correct that Gore-Tex is a physical membrane. Jackets aren't made of Gore-Tex, they are made with various face-fabrics, some better quality, some lesser. The membrane is bonded to the inside of that fabric.

The point of Gore-Tex vs other waterproof membranes is that is quality control of it's breathability. There are 2 ways you can lose this breathability.

Normally the face fabric is bonded/coated with a layer of DWR (durable water repellent), sorta like TEFLON. It's hydrophobic and just makes the water bead off. But this coating eventually wears out from abrasion or just movement of the fabric fibers.

There are 2 ways your Gore-Tex jacket will fail at it's job of waterproof-breathability.

1. That DWR is degraded. So now your face fabric is completely sogged like a pair of wet jeans. This is called wet out. Now you've got a solid sheet of water over in the face fabric and your jacket can't breath. The spray is to refresh your DWR and keep water beading off your jacket.

2. Your Gore-Tex membrane gets clogged up with grime, dirt and body oils. Again, no more breathability. It's dirt that you need to remove with detergent.

Hope this helps!