Move test base class for web_applications code to c/b/picture_in_picture

This CL moves the existing test base class that is used to verify
document picture in picture functionality to
chrome/browser/picture_in_picture, so that it can be reused across all
areas of Chrome. This is going to be useful when the Create Shortcut
dialog's interaction with picture in picture windows is going to be
fixed.

Currently it only builds on non Android builds due to requirement and
usage.

Bug: 352610623
Change-Id: I10dc4c4bf84335e9b9017abcfb8c5dcb4f1a4328
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5703237
Reviewed-by: Tommy Steimel <steimel@chromium.org>
Commit-Queue: Dibyajyoti Pal <dibyapal@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1327617}