[devtools] Attempt to de-flake and re-enable style test

The CL re-baselines and re-enables the styles-4/style-update-from-js.js
web test. The order of properties has changed, so the new baseline
accounts for that. Moreover this CL refactors the test to use
the promisie-fied versions of test helpers, hopefully reducing
the past flakiness.

R=alexrudenko@chromium.org

Bug: 946716
Change-Id: Ic5720685d634a2f749cb8d2468bcb894620affcf
Fixed: 794869
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4456576
Commit-Queue: Simon Zünd <szuend@chromium.org>
Reviewed-by: Alex Rudenko <alexrudenko@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1133739}