Hmm, should this forward the user back to the initial page? It could also be used to filter the cards on the shortcuts page, which I could see being useful if someone has like 30 extensions installed.

Thoughts?

Having the search box do a different thing based on the current page, can be confusing I think (in-page searchboxes are more appropriate for that task). 

Instead having the toolbar's search box do a single thing, regardless of where it is invoked from, seems simpler and probably sufficient (and it is what Settings  does). Basically I am suggesting:

When user searches, always forward to the initial page and perform a search there. We should probably add the search parameter in the URL, such that "back" and "forward" work with search, as well as direct navigation to a search URL.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/6719bcfd8b8dcffed3fa08d56602ebdbe0e62f54

commit 6719bcfd8b8dcffed3fa08d56602ebdbe0e62f54
Author: Scott Chen <scottchen@chromium.org>
Date: Thu Oct 19 21:11:23 2017

MD Extensions: navigate to list view when searching.

Bug:  769572 
Cq-Include-Trybots: master.tryserver.chromium.linux:closure_compilation
Change-Id: I87beab786bcc3644290ff555994af980f3dbe59d
Reviewed-on: https://chromium-review.googlesource.com/723610
Reviewed-by: Dave Schuyler <dschuyler@chromium.org>
Commit-Queue: Scott Chen <scottchen@chromium.org>
Cr-Commit-Position: refs/heads/master@{#510214}
[modify] https://crrev.com/6719bcfd8b8dcffed3fa08d56602ebdbe0e62f54/chrome/browser/resources/md_extensions/manager.js

Verified the fix on Mac 10.12.6, Win-10 and Ubuntu 14.04 using latest chrome version #64.0.3247.0 as per the comment #0.
Attaching screen cast for reference.
Observed that the search was successful at chrome://extensions/shortcuts as expected.
Hence, the fix is working as expected. 
Adding the verified labels.

Thanks...!!

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