I would say it’s even more important in the case of a web app that stores data locally, because it’s imperative that the user understands that data is tied to that particular web browser and device, and that clearing site data (which I’ve known non-technical users to do periodically to reduce tracking footprint), changing devices, etc can/will result in data loss.

Oddly enough the handful of web apps I’ve known to use local storage don’t communicate this at all. Developers seemingly treat data in browser local storage as existing indefinitely and unlikely to be deleted, when in fact it’s probably the most easily accidentally lost form of storage an app can have.