[omnibox][lens] Fix broken zero-prefix UX in CSB.

The introduction of the `OmniboxZeroSuggestSynchronousMatchesOnly`
appears to have broken the zero-prefix experience in the Lens overlay
(CSB). This CL fixes the issue by limiting the scope of this feature
such that it will only impact the "ZPS on Web" experience, which is
precisely the page context where "Contextual Search in Omnibox" is
currently active.

Bug: 420721378
Change-Id: I1c0e8d3e044ec762dee7dc91272e2a0942086177
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6599036
Commit-Queue: Khalid Peer <khalidpeer@chromium.org>
Reviewed-by: Duncan Mercer <mercerd@google.com>
Cr-Commit-Position: refs/heads/main@{#1466812}