It looks like this works by making the browser use dn as a local proxy. That should also work with non-chromium based browser right ? I guess it will then be necessary to configure the proxy manually.
You could do something similar with a proxy, but it may run into issues with HTTPS, which this gets around as we are beyond the terminator. In this way, you can serve the content, and save the content, via getting in the middle of the same fetch process and the browser doesn't know the difference (mostly).
There's also somewhat equivalent surface exposed by WebDriver BiDi: https://w3c.github.io/webdriver-bidi/#module-network-command...
If you want to read more about these sorts of protocols, see: https://firefox-source-docs.mozilla.org/remote/index.html