Migrate the VS Code Sidebar API to use the Dart Tooling Daemon

[kenzieschmoll]

Using postMessage was a workaround that we used in the absence of DTD. Now that DTD is finishing up, we will be able to migrate away from postMessage for the VS code sidebar, which will be more robust and will allow us to use standalone UI components outside of an embedded environment.

@DanTup

[kenzieschmoll]

@DanTup this work is complete, right? If so we can close this issue.

[DanTup]

The DevTools work is done, but the Dart-Code work isn't complete yet - we need to pick an SDK version to gate it on and remove the preview flag. I've opened Dart-Code/Dart-Code#5225 to track changing that over, feel free to close this if you don't think we also need it.

We should also perhaps open an issue above removing the postMessage version of sidebar in a future SDK (I think we want to wait for at least a stable release and several months of Dart-Code being out using the DTD sidebar without a preview flag before doing that).

Edit: Looks like DevTools hasn't rolled into the SDK yet since the DTD sidebar change landed (https://github.com/dart-lang/sdk/blame/main/DEPS#L105 currently shows 2.38.0 was last rolled in, but the sidebar is first in 2.39.0-dev.0).

[DanTup]

(this was completed some time ago)