[lensoverlay] Add field for whether thumbnail should be shown in the side panel.

LensOverlaySidePanelCoordinator::NotifyNewQueryLoaded() should
canonically determine whether the thumbnail should be shown for the
current query by checking for the Lens mode parameter. However,
LensSearchboxController::OnThumbnailProcessed() gets called regardless
of whether the thumbnail should be shown, and if this happens after
NotifyNewQueryLoaded(), the thumbnail will appear even when it
shouldn't. Address this by having NotifyNewQueryLoaded() set a boolean
in the init_data which determines how the side panel thumbnail is
handled.

Bug: 440653648
Change-Id: Ib8edc6537af6592a42e03f4288b150bed3b8ad61
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6920451
Reviewed-by: Juan Mojica <juanmojica@google.com>
Commit-Queue: Bryan Nguyen <nguyenbryan@google.com>
Cr-Commit-Position: refs/heads/main@{#1512788}