LibWebView: Protect the Inspector against rapid inspection requests
This was seen in Browser when hotkey activations were processed twice.
If we open the Inspector with a hotkey (F12) and quickly activate that
hotkey again, we could try sending a JS command (inspector.loadDOMTree)
before the inspector.js file was actually loaded in the WebContent.
The window for this bug is larger on Serenity, where loading WebContent
is a bit slower than on Linux. So even with the Browser bug fixed, it is
pretty easy to hit this window still.