Present the ScreenCaptureKit window/screen picker with `-[SCContentSharingPicker presentPickerUsingContentStyle:]
<rdar://problem/113424298>
Pull request: https://github.com/WebKit/WebKit/pull/16416
Committed 266640@main (3eac88b8c6c7): <https://commits.webkit.org/266640@main> Reviewed commits have been landed. Closing PR #16416 and removing active labels.