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.
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.