Stop erasing Window picker option when using PipeWire

Now that we have the ability to control whether or not the PipeWire
picker is visible; we can also re-split that Picker from one that shows
both Screens and Windows to one that shows either screens or windows.
This allows us to remove some of the customization we had previously
had to do for the PipeWire picker and should remove some edge cases
when dealing with that picker.

Bug: 1351570
Change-Id: Ia676e35dff0a84d7e9363d42060d2c502c6510a9
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3864873
Reviewed-by: Elad Alon <eladalon@chromium.org>
Commit-Queue: Alexander Cooper <alcooper@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1042803}