Try https://usebx.com/app - we built it 2 years ago. It's a PWA, and our users find it better than many native alternatives. I think it's all in the execution really.
Also (but this is more of a niche problem with more technical users) I wouldn't have noticed it's a PWA if you hadn't told me since I block service workers by default. I would, however, have noticed a banner taking me to an app store of your choice.
Still, the app itself is cool though. Maybe you can use touch gestures on the web after all ;)
Not currently, but it's not a bad idea to write something. As soon as I get a spare few hours, I will put something together. Feel free to drop me an email (see profile) and I'll notify you when it's done.