Reland "[CHAP] Add BrowserInitiatedAutomaticPictureInPicture to chrome://flags"

This is a reland of commit 51e04dc75a78e8712fcdb2a64730eed442399ad8

This reland does not modify any files, since the original issue was
fixed on
https://chromium-review.googlesource.com/c/chromium/src/+/6465615.

Original change's description:
> [CHAP] Add BrowserInitiatedAutomaticPictureInPicture to chrome://flags
>
> Bug: 408502322, b/318568892
> Change-Id: I38ffd826498584c195f6a1118cd65513efc985de
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6437622
> Commit-Queue: Benjamin Keen <bkeen@google.com>
> Reviewed-by: Frank Liberato <liberato@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1447469}

Bug: 408502322, b/318568892
Change-Id: I58a4730895de1ae4e962179fe595edd542fe04ce
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6470322
Reviewed-by: Frank Liberato <liberato@chromium.org>
Commit-Queue: Benjamin Keen <bkeen@google.com>
Cr-Commit-Position: refs/heads/main@{#1449090}