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This property was replaced with the UI blocker abstracted in a protocol
in crrev/2288853 but it was still used in a few places, thus that CL
introduced bugs, including potentially showing sign in promo when the
blocking UI is shown, and switch-to-open-window button never working.

Remove this property and replace it by extending UIBlocking* protocols.

Bug: 1103565
Change-Id: Ib79d2968c1fe545ef5cd87cc196802ad6097345c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2398684Reviewed-by: Sylvain Defresne <sdefresne@chromium.org>
Commit-Queue: Stepan Khapugin <stkhapugin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#805270}