From the manual:
WebStorage does not store in the browser cache. If the user opts to empty the browser cache, WebStorage data remains intact. However if the user opts to clear all their cookies or offline website data,
WebStorage will be cleared
Can I just say that based on my own current frustrating and project stalling experiments with attempting to use local 'webstorage' to store level data, I don't think it is suitable at all for storing level data created by the game dev.
Level data as in data created by the developer of the game to set up multiple levels - afaik that level data won't be 'shipped' with your exported game because webstorage is designed to save and load data created within the game - but the data is not created within the game - only accessed by the game and possibly created by an editor created to support development.
More detailed information is needed in the manual about the different ways to store files externally. For example - Where is the data stored?
I'm storing the levels I create using my level editor in an array (grid x, grid y, and sheet number) and I want to have several packs available on release day with the option to add extra packs later.
Webstorage just seems totally irrelevant in my case and possibly in the OP's case.
Download and Load as json also misses the mark - In all my attempts at storing an array as json and 'downloading' that file, When I run the program again any changes I made are gone - because the last saved file has to be re-imported to the project for the changes to be available.