Comprehensive integration tests for new inspector

One of the things we need to test is whether auto-refreshing of the inspector tree works as expected after editing code and performing a hot-reload. For this, we will need a live app connection, along with either a real or fake editor so that we can modify code.

Whatever solution we come up with here will also be beneficial for testing the property editor integration across Devtools, the IDEs, and the Analysis Server.

Start by locating the new inspector integration-test entry points and the code paths for the inspector tree, live app connection, hot-reload, and editor interaction. Done means verifying auto-refresh after code edits and hot-reload, with either a real or fake editor, and covering property-editor integration across DevTools, IDEs, and the Analysis Server.

Written by the indexing model from the issue text.