Nah, that's not gonna do anything for this given it is looking at the I/O characteristics of your SSD, it doesn't need any permissions to do this, it's basically just copying stuff in its own sandbox and pulling data from analysing the transfer characteristics.

Unless for every site you want to visit you install a fresh SSD, with a new installation of a browser and you only ever visit a given site from its dedicated browser and SSD, and do nothing else with it. (This is not limited to figuring out just what sites you're visiting, but also what applications you're ruining)

The alternative is something similar to what I suggested which is to basically ensure your SSD is spammed with accesses so it's very hard to pull out the individual signals.

It's similar to a VPN connection. If someone is particularly interested in you, they can look at the pattern of VPN transfer traffic. If you open a connection and then go straight to a website and nothing else, it's relatively trivial for a determined enough adversary to take a fingerprint of the transfer sizes and timings. Enough times they can get a good set of fingerprints that they can then start to match to actual sites.

Now this was regarded as quite hard to do until AI tools like this one come along to dramatically reduce the time needed to do this analysis.

A way to mitigate the above is to make sure your connections are doing multiple things so it's harder to pull these fingerprints from traffic patterns. So I'm assuming the same strategy would work here given it's basically the same kind of attack