Set Runner on CopyOutputRequest when added

This is for SingleThreaded mode only (thus, ui/compositor only).

Bug: b/324199451
Change-Id: I01c7670146be21a058d54cc0a88210ec7a9173d2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5287895


Reviewed-by: Kyle Charbonneau <kylechar@chromium.org>
Commit-Queue: Mitsuru Oshima <oshima@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1270647}