Rework `network-audit` into a browser test suite

[bsclifton]

Description

See #7207 for history

Until #7182, all platforms were killing the browser during network-audit using SIGKILL. This doesn't let the browser finish writing the logs and requires a manual work-around to make the logs parseable. The integrity of those logs is then questionable

While solving, @bridiver mentioned creating a new test suite, something like npm run test brave_network_audit that would accomplish the same thing as this test. That could then be expanded to run other scenarios (which also accumulate in that log)

from @bridiver

I think the best fix for this is to turn it into a browser test that runs with a separate command. I pointed @bsclifton to LogNetLogTest which tests the basic functionality so we can use that as a template and add our checks. I think it's also better because we can do navigation, etc... that might trigger other requests