I created an SRS based kanji learning app (https://shodoku.app/ https://github.com/runarberg/shodoku) hosted on GitHub Pages (meaning the app is a static HTML page) where all the dictionary data is stored as hundreds of thousands of json (and SVG) files. Storing these assets using the Cache API saves tens of thousands of round trips to the server in addition to offering a somewhat robust offline experience.
It's very powerful, which also makes it a footgun: you can end up with fetch() requests going out over the network, with server responses saying one thing, but the frontend receiving something completely differently.
As for examples, I believe Home Assistant uses it to cache pretty much every resource in the frontend pre-emptively so you can use the web UI even if your internet connection is down (but your connection to your home server isn't).