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If (like in tests), entering tablet mode requires taking a screenshot, we need
to rebuild property trees and submit the copy request to viz. Without
allowing nested tasks, this can't run and we get a deadlock.

Bug: b/139186625
Bug: b/135956156
Test: tast -verbose run dut-4 arc.PIP passes
Change-Id: I4af9836fa562835e6d866015ceeaf47772e4270c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1753783Reviewed-by: Mitsuru Oshima (OOO 8/12,13) <oshima@chromium.org>
Commit-Queue: Eliot Courtney <edcourtney@chromium.org>
Cr-Commit-Position: refs/heads/master@{#686725}