Doesn’t that require you to host it and have it available on the open web, though? Is there a host that allows you to, for free, not only HTML/CSS/JS but also access to arbitrary tools and bespoke scripts on the backend?
For free? No, but if you built a native app that needed a backend, you'd still need to host the backend somewhere too. I host my own web apps from a cheap mini pc at home and access them over tailscale for personal use.
That's true for most things where you don't need users to share or collaborate on updated data. But if you need so much as a highscore board for your casual javascript game, you need some kind of backend. The parent's assumption that it should be totally free to run arbitrary server code somewhere is mildly ridiculous.
I'm pretty sure that if you build your PWA in a way it works offline through caching (which is easy if it's just a static website), you could host/serve it temporarily and just install it once.
As a lark, I built a set of personal productivity apps that are delivered as standalone local webpages. Works surprisingly well on Android, haven't tested on iOS.