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Add search metrics reporter for the new sandboxed Index. The logic is
similar to what we have done with IndexSync.

Design doc: go/lss-sandboxing
Implementation plan: go/lss-sandboxing-impl

Bug: 1137560
Change-Id: I4f54cf8eaa0f0f54db0e64b71749ea87c860d26f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2569563Reviewed-by: Jia Meng <jiameng@chromium.org>
Commit-Queue: Thanh Nguyen <thanhdng@chromium.org>
Cr-Commit-Position: refs/heads/master@{#833221}