This is the proper answer: when water soaks the outer (non-GoreTex) layer, it doesn't breath anymore. One of GoreTex's fixes for that was to introduce jackets that don't have the outer (or inner) layer(s). It's just one big sheet of GoreTex "laminate" without being laminated to anything. "GoreTex Shakedry" is the search phrase you want, though they don't make the jackets anymore (because aforementioned "forever chemicals").

It's unfortunate, too, because the Shakedry jackets are what Gore has been promising for 50 years: waterproof yet breathable. I have one, and I am going to be very sad when it gets retired. Packs small, completely waterproof (I've used for 50 mile running races and stayed bone dry), yet breathable so you don't stew in your own juices (see "50 mile race" above).