Is PFOS / Gore Tex a health hazard if I wear it instead of eat it?

It’s not even a health hazard if ingested. That’s not the issue with the stuff.

What are the non gore tex alternatives and how do they stack up to gore tex and each other?
Are any of the gore tex alternatives better or safer than gore tex?

There’s a quick graph, F9 has more in-depth reviews of specifically motorcycle gear in their videos. They’re a motorcycle (and recently bicycle) channel, not a “here’s this piece of tech and I’ll explain it” channel, though they do end up doing a lot of that.

As to the safety aspect: Gore-Tex isn’t PTFE any more, it’s PE/PU like the rest. Dead dinosaurs, probably microplastics but not forever chemicals.

Should I really just use a sweater and/or a plastic bag?

You should also wear a baselayer. A material that wicks well as base (linen or merino are good, polyester is cheap but can easily get smelly), then something insulating, with lots of air in it, as mid-layer and make sure that it’s not tight because that doesn’t vibe with having air in it, then a shell layer which material-wise is more important to be waterproof than breathable: You can have flaps etc as water doesn’t tend to fall upwards.

A sweater and appropriately tailored plastic bag thus isn’t a bad start, modulo that your probably cotton t-shirt as a baselayer isn’t a good idea, it’ll get wet from your own sweat and then you’ll be cold.

This was not the deep analysis I think this topic needs.

That would be a fucking dissertation. But I have something for you.