This post has some discussion on it. The tl;dr is that for a BIFL item, you need to ask yourself if you need a hiking jacket that is water resistant and can breathe, or if you need an actually waterproof jacket that doesn't breathe.
If you want a hiking jacket, they are mainly a consumable item, but you can get some that hold up better than others; look for a 3 layer construction. I'd really advise not using a hiking jacket as a "walking around town" jacket.
For a "walking around town" jacket, you can go with an oiled or waxed fabric if you want to stick with non-synthetics. If you are okay with synthetics, you can go for a polyurethane jacket that is 100% waterproof. Polyurethane rain jackets seem to have fallen out of favor over the past 25 years as people have preferred lightweight goretex jackets with PFAS coatings. I googled around to see who even makes good PU jackets, and it looks like despite being a otherwise pricy brand, Helly Hansen makes cheap PU jackets.