VideoPlayer widget is sometimes falling back to the first stream when two are present

This was reported by Blake.
It caused a lot of confusion, since he had already configured video widgets for his two streams, and then, out of nowhere, he had the same stream playing in both widgets.

The issue does not name a file, test, entry point, or reproduction steps. Start by locating the VideoPlayer widget and the stream-selection logic, then reproduce the case with two configured streams and verify that each widget consistently plays its assigned stream.

Written by the indexing model from the issue text.