WebUI Searchbox: Restore onResultRepaint_ invocation in the Lit version.

The invocation was accidentally removed in the Polymer->Lit migration CL
at https://crrev.com/c/6968638.

Having said that, previously this was invoked on Polymer 'dom-change'
events which don't have a direct equivalent in Lit. The closest
equivalent is the 'updated' lifecycle callback which executes after each
asynchronous rendering cycle of a Lit element, so the recorded metrics
are likely to be a bit different than before.

Bug: 445727122
Change-Id: Ic2d1bcece3a84f5f333d4811dd86a33c9cd48415
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6974987
Auto-Submit: Demetrios Papadopoulos <dpapad@chromium.org>
Reviewed-by: Moe Ahmadi <mahmadi@chromium.org>
Commit-Queue: Moe Ahmadi <mahmadi@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1519056}