As a guy who makes most everything in HTML, CSS, and JS I still don't understand the logic of it will be lightweight and fast, given how many crappy things that are not lightweight and fast I see all the time in the web stack.

It'll have more performance is the correct argument, if you can prove it. But I have my strong doubts. I would make the argument on

it will be easier to develop and maintain because you will have a unified stack. Meaning it will be cheaper. If you increase performance in one you will probably increase performance in the other, meaning the work you do to increase performance in your website will probably translate into performance improvements in your app.

I (a web developer) do not find HTML/CSS/JS easier than native development tbh. It's just a lack of familiarity that pushes people to use javascript for absolutely everything (despite it being unsuitable for many of those tasks).

I feel the same when I see people arguing that ESP32 class processors should only be written in Assembly and C, having used high level languages on MS-DOS, Amiga and ZX Spectrum compatible hardware.

A progressive web app also includes a manifest.json file to define how the app launches when it's installed, a service worker for background operations, app icons for the user's device homescreen, etc. An HTML5 app and a PWA are similar but really they're not the same. https://developer.mozilla.org/en-US/docs/Web/Manifest

Not really, because thanks to the manifest.json, and if packed as stored app, it also has access to OS APIs, exposed in the browser.