Fix race condition in colorenhancer extension

AX-Relnotes: n/a.
Bug: 1289423
Test: Manually inspected the extension behavior (it's unchanged)
Change-Id: I1b7212bb769ff7594767ed2067428117b876a04a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3413494


Auto-Submit: Anastasia Helfinstein <anastasi@google.com>
Reviewed-by: Josiah Krutz <josiahk@google.com>
Commit-Queue: Josiah Krutz <josiahk@google.com>
Cr-Commit-Position: refs/heads/main@{#963054}