Revert "Reland "[lens-rearch][30/n] Remove update context from overlay controller.""

This reverts commit cac2493a61bad3b74ba3925c4dca9a266a798cae.

Reason for revert:
LUCI Bisection has identified this change as the cause of a test failure. See the analysis: https://ci.chromium.org/ui/p/chromium/bisection/test-analysis/b/6269741137133568

Sample build with failed test: https://ci.chromium.org/b/8714130360255361761
Affected test(s):
[ninja://chrome/test:browser_tests/LensOverlayControllerInnerHtmlWithInnerTextAndApc.PageContentTypeHistograms](https://ci.chromium.org/ui/test/chromium/ninja:%2F%2Fchrome%2Ftest:browser_tests%2FLensOverlayControllerInnerHtmlWithInnerTextAndApc.PageContentTypeHistograms?q=VHash%3A6d0a43807ac672d9)

If this is a false positive, please report it at http://b.corp.google.com/createIssue?component=1199205&description=Analysis%3A+https%3A%2F%2Fci.chromium.org%2Fui%2Fp%2Fchromium%2Fbisection%2Ftest-analysis%2Fb%2F6269741137133568&format=PLAIN&priority=P3&title=Wrongly+blamed+https%3A%2F%2Fchromium-review.googlesource.com%2Fc%2Fchromium%2Fsrc%2F%2B%2F6575884&type=BUG

Original change's description:
> Reland "[lens-rearch][30/n] Remove update context from overlay controller."
>
> Differences from reverted version: These changes by viewing the diff
> from PS1 to the latest PS. The differences are the disabling of the
> failing tests on branded builds with an added TODO that they should be
> re-enabled and fixed when fully resolving crbug.com/417812533
>
> This is a reland of commit f213852e1756254a740b6de1b4435ad88f9175e4
>
> Original change's description:
> > [lens-rearch][30/n] Remove update context from overlay controller.
> >
> > This removes the update page contextualization code from the overlay
> > controller in favor of updating the page context via the
> > contextualization controller. This also removes the overlay controller
> > not showing the overlay when initializing. This should be a no-op.
> >
> > Bug: 418825720
> > Change-Id: I3f559650c7d67f2cb9b62e9639b8907e9035a886
> > Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6565474
> > Commit-Queue: Juan Mojica <juanmojica@google.com>
> > Commit-Queue: Duncan Mercer <mercerd@google.com>
> > Reviewed-by: Duncan Mercer <mercerd@google.com>
> > Auto-Submit: Juan Mojica <juanmojica@google.com>
> > Cr-Commit-Position: refs/heads/main@{#1463558}
>
> Bug: 418825720
> Change-Id: Ief6b9e2c41ff5a34145c2d796699933842ffa189
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6575884
> Auto-Submit: Juan Mojica <juanmojica@google.com>
> Reviewed-by: Duncan Mercer <mercerd@google.com>
> Commit-Queue: Duncan Mercer <mercerd@google.com>
> Cr-Commit-Position: refs/heads/main@{#1464392}
>

Bug: 418825720
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Change-Id: Iafd8a49eb833ed7574c990d2095e5f39a120d58c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6581378
Owners-Override: Yoshisato Yanagisawa <yyanagisawa@google.com>
Commit-Queue: Yoshisato Yanagisawa <yyanagisawa@chromium.org>
Reviewed-by: Yoshisato Yanagisawa <yyanagisawa@chromium.org>
Reviewed-by: Lingqi Chi <lingqi@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1464598}