Research potential problems and ways to rewrite subsystems in Hammerhead to implement proxy-less mode

[AndreyBelym]

We should know how fast we can build a proxyless prototype. We should check what problems we can get.

• [x] #6830
• [x] Rewrite remaining TestRun messages handlers to use CDP
• [x] Rewrite BrowserConnectionGateway message handlers
• [x] Refactor and remove dead code (in the TestCafe class)

[miherlosev]

Done