Ensure embedded window's channel is not disposed before being duped

If the InputChannel is created inside a critical section, but then
duped to another channel after the lock is released, it's possible
the channel could be disposed (e.g. because window is removed) before
the duplication happens. To prevent this, dup the InputChannel in the
same critical section as where it was created.

Bug: 283314325
Test: Presubmit
Change-Id: I00dd3e54240512a6d2ddfe7ec40a6c4f14d837fc