A first step would be opt-in UKM and analyze the data.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/734479549491fecd4b3d53047d6286b6108305d6

commit 734479549491fecd4b3d53047d6286b6108305d6
Author: Takayoshi Kochi <kochi@chromium.org>
Date: Tue Jun 05 08:34:56 2018

Opt-in Shadow DOM v1 and Custom Elements v1 to UKM

To analyze usage distribution and major users, opt-in
Shadow DOM v1 and Custom Elements v1 API UMA into UKM.

Bug:  848153 
Change-Id: I262ea5628cfc96325b1d22a41d0c3a83cbe969f3
Reviewed-on: https://chromium-review.googlesource.com/1080432
Commit-Queue: Takayoshi Kochi <kochi@chromium.org>
Reviewed-by: Robert Kaplow <rkaplow@chromium.org>
Cr-Commit-Position: refs/heads/master@{#564408}
[modify] https://crrev.com/734479549491fecd4b3d53047d6286b6108305d6/chrome/browser/page_load_metrics/observers/use_counter/ukm_features.cc

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/30a88fb245c1056b3ec261ba3699d13b6f0fd900

commit 30a88fb245c1056b3ec261ba3699d13b6f0fd900
Author: Takayoshi Kochi <kochi@chromium.org>
Date: Mon Jul 09 06:00:06 2018

Opt-in Polymer's usage counter to UKM

To analyze any popular sites that use Shadow DOM V0,
Custom Elements V0, HTML Imports APIs without
using Polymer's polyfill, use Polymer's counters
for excluding from those sites collected for
Shadow DOM V0, Custom Elements V0, HTML Imports API
raw usages.

Bug:  848153 
Change-Id: I9ba3c70b06cd376157f3788e029373673bbcd1cd
Reviewed-on: https://chromium-review.googlesource.com/1127575
Reviewed-by: Robert Kaplow <rkaplow@chromium.org>
Commit-Queue: Takayoshi Kochi <kochi@chromium.org>
Cr-Commit-Position: refs/heads/master@{#573227}
[modify] https://crrev.com/30a88fb245c1056b3ec261ba3699d13b6f0fd900/chrome/browser/page_load_metrics/observers/use_counter/ukm_features.cc

The rest of this task is to analyze the data.
Code/stat collection changes are in.