Create a way for users to try beta or master DevTools without having to switch their flutter version

Since we ship DevTools with the flutter SDK, we often run into a latency issue where we have shipped a DevTools version on Flutter master that has bug fixes users are interested in (e.g. the network page fixes of recent), but users have no way to try this DevTools version out unless they switch to the flutter master channel. This can be problematic for users, as they may not be able to switch to the master channel without a big lift.

We should design a way for users to try DevTools from Flutter Beta or Flutter master at the click of a button in DevTools. We will not be able to guarantee that this DevTools version will be compatible with the user's Flutter version, but we can warn users about this.

No files, tests, or entry points are named. Start by tracing how DevTools is bundled and selected with the Flutter SDK, then define the user flow for trying Beta or master and the compatibility warning. Done means users can choose those DevTools versions without changing their Flutter channel.

Written by the indexing model from the issue text.