Apps can be free of app stores as well. You can install it directly from GitHub.

PWAs are bloaty. press F12 and click the "sources" tab (assuming chrome or derivative here) and look at all the scripts that have to load. Some of that is for the Service Worker.

And then click the overflow, if it's a usual narrow side pane in the debug interface, to "memory" tab. It will also show you how buch data it is pulling down. Constantly the service worker is precaching assets and the like.

PWAs are as heavy as apps running on Electron (eg discord, many others). They literally bump up against the small memory available on older phones and spend a lot of time doing things to work around the lack of free space. Actually, they are usually even worse, because with electron apps often there is a native compiled backend running the storage and app logic, whereas the PWA every bit of code is javascript.

For these devices it would make more sense to have a javascript free old school version, same look, just not so many active interactive/animation features, and it'll load up in about 40kb if you use Svelte (this site uses svelte, but it's a PWA).

So an app is a good thing. And it's gonna be consistent whereas the PWA is gonna be a bit wonky on old gear. There is so few features this thing requires, I think it only needs network and disk access permission, at most.