> anything privacy sensitive

I'd actually prefer that stuff stay in a browser and far away from my local storage on a device I take everywhere. Seems far riskier having it locally.

> anything processing intense

I can play Half-Life 2 in a browser window these days. I can do photo editing and CAD in the browser. I can have entire IDEs in the browser, compilers, non-linear video editors, and more. We're also kind of scoping this to phone apps, they're usually not very processing intense as you quickly hit heat and battery limits.

> camera and audio based features can work, but are more finicky (or outright broken on ios)

Sounds more like an overly restricted OS than anything else.

> local storage (exists in web app, short lifetimes on web site)

Once again, sounds like an overly restricted OS than a browser issue.

> (I'm less familiar, but probably local sensors, like gps and acceleration)

https://sensor-js.xyz/demo.html < works fine

https://openstreetmap.org < works fine