Looks like the WebContents version is only called from OverlayPanel, which it appears mdjones@ added:
https://cs.chromium.org/chromium/src/chrome/android/java/src/org/chromium/chrome/browser/compositor/bottombar/OverlayPanel.java?type=cs&q=updateBrowserControlsState&sq=package:chromium&l=440

OverlayPanelContent seems to have native methods, so it looks like we could just add a new native method that would call the similar behavior that was changed in Tab.  That should be callable from anywhere in the chrome layer right?

In flight patch:
https://chromium-review.googlesource.com/c/chromium/src/+/917218

I'm not going to be handling interstitial pages since the class in question isn't intended to display them. Though if anyone objects to that I can add the logic. I'll handle the unused path cleanup in a follow-up.

Clean up patch here:
https://chromium-review.googlesource.com/c/chromium/src/+/917329

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/67cbdeb0a26d26b4b033f89dbb5603e061bd9964

commit 67cbdeb0a26d26b4b033f89dbb5603e061bd9964
Author: Matthew Jones <mdjones@chromium.org>
Date: Thu Feb 15 19:36:49 2018

Replace browser controls update in OverlayPanelContent

This change replaces the browser controls update logic in overlay
panels with a native mojo version. This was the only usage of
updateBrowserControls in java web contents which can now be removed.
The number of parameters used by the function in OverlayPanel has been
reduced to handle how it is being used -- either completely shown or
completely hidden.

BUG= 810937 

Change-Id: If17709f43a150dec30b0b9cd0644161b1f5ad265
Reviewed-on: https://chromium-review.googlesource.com/917218
Commit-Queue: Matthew Jones <mdjones@chromium.org>
Reviewed-by: David Trainor <dtrainor@chromium.org>
Cr-Commit-Position: refs/heads/master@{#537100}
[modify] https://crrev.com/67cbdeb0a26d26b4b033f89dbb5603e061bd9964/chrome/android/java/src/org/chromium/chrome/browser/compositor/bottombar/OverlayPanel.java
[modify] https://crrev.com/67cbdeb0a26d26b4b033f89dbb5603e061bd9964/chrome/android/java/src/org/chromium/chrome/browser/compositor/bottombar/OverlayPanelContent.java
[modify] https://crrev.com/67cbdeb0a26d26b4b033f89dbb5603e061bd9964/chrome/browser/android/bottombar/overlay_panel_content.cc
[modify] https://crrev.com/67cbdeb0a26d26b4b033f89dbb5603e061bd9964/chrome/browser/android/bottombar/overlay_panel_content.h

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/b4456421b708df741adf44a137e76b943222d398

commit b4456421b708df741adf44a137e76b943222d398
Author: Matthew Jones <mdjones@chromium.org>
Date: Thu Feb 22 20:29:41 2018

Remove unused browser controls IPC path

BUG= 810937 

Change-Id: I0cc6b8c92f1d71cd127d9bc35e0159eeff35b2e1
Reviewed-on: https://chromium-review.googlesource.com/917329
Commit-Queue: Matthew Jones <mdjones@chromium.org>
Reviewed-by: John Abd-El-Malek <jam@chromium.org>
Reviewed-by: Daniel Cheng <dcheng@chromium.org>
Reviewed-by: Ted Choc <tedchoc@chromium.org>
Cr-Commit-Position: refs/heads/master@{#538547}
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/browser/web_contents/web_contents_android.cc
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/browser/web_contents/web_contents_android.h
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/common/view_messages.h
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/public/android/java/src/org/chromium/content/browser/webcontents/WebContentsImpl.java
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/public/android/java/src/org/chromium/content_public/browser/WebContents.java
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/public/test/android/javatests/src/org/chromium/content/browser/test/mock/MockWebContents.java
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/renderer/render_view_impl.cc
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/renderer/render_view_impl.h
[modify] https://crrev.com/b4456421b708df741adf44a137e76b943222d398/content/renderer/render_view_impl_android.cc