It may actually end up stronger, I fixed a friends glasses with superglue, next time she sat on them it broke in a different place.

Superglue is pretty strong stuff.

Could try the old superglue-with-baking-soda trick. I've had people recommend it to fix moveable parts in stereo equipment, apparently it turns hard as concrete.

I had the exact same problem and tried that first, but it did not work in my case: There was a strong pull on it, and the surfaces did not fit perfectly.

If the surfaces fit perfectly, OP can try. Superglue (most / some types) can be removed later from the glasses, but of course, no harm avoiding that in the first place.

These are made of polycarbonate. Cyanoacrylate glue is the only option, but honestly, there are thousands of similar glasses to these and they are cheap.

That is the way to go. I used a different 2 component glue, and it holds perfectly. Nothing else worked.

Only if there is a real gap that needs to be filled, rather than two perfectly fitting surfaces, gradually filling it with a 2 component glue like this might work better: https://hgpowerglue.com/collections/bestseller/products/schweissnaht-aus-der-flasche-regular

Tried with UV hardening glue first, but the problem was that it "slipped" from the material, so the glue piece came off as a whole. I should have used sandpaper on all surfaces first.