Build a long-running web integration test running in HTML/CanvasKit and debug/profile/release modes. The goals of the test are:

• Running for a long time will expose memory leaks.
• Running in all mode combinations covers critical user journeys w.r.t. building and running an app.

The test should exercise an app representative of real-world usage. Ideally it would be the new gallery. However, given the difficulties with managing dependencies between flutter/flutter and flutter/gallery, starting with the old gallery should be fine for now.