Firefox 100 (at least) has an about:cache which doesn't give you most of the stats you want, but does give you some usage information anyway. The last-modified date it reports doesn't seem correct at least when looking at the disk cache.

To get the stats you want, you'd probably need to write a plugin using one of the hooks that lets you see all the requests (which are being phased out, but such is life).

Depending on your flows, you might be able to use <link rel="prefetch"> on a corporate home page to try to get things loaded, before users get to your app, although no guarantees of course.