Marking the test as slow, it finishes but actually fails.

FAIL Test that the overlay cast button fades at the right time (neither too soon nor too late). assert_true: button should exist expected true got false

Seems like the overlay button has been broken for some time :/
In RefreshCastButtonVisibilityWithoutUpdate there's a comment that says we don't show the overlay cast button for autoplay videos that has been paused (on Android) as these tend to be background decorative videos. However, the check on the code states:

if (!MediaElement().ShouldShowControls() && !MediaElement().Autoplay() && MediaElement().paused()) {
  .. try to show the overlay button
}

This check excludes any playing media or autoplay muted media when paused from getting the overlay button shown ever. It should be !(MediaElement().Autoplay() && MediaElement.paused()) to match what the comment says.

Given we allow autoplay muted which is what'd be used for the background animation, we probably should not show the button for this. If it's an audible autoplay video we paused, showing an overlay cast button for it sounds like a good idea (as another way to play the video somewhere). 

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/e8a72f003a04193cdacbeac76d9c5cb86e15072e

commit e8a72f003a04193cdacbeac76d9c5cb86e15072e
Author: Anton Vayvod <avayvod@google.com>
Date: Fri Jun 09 04:03:36 2017

Fixed controls-cast-overlay-fade-slow.html

Fixes the code checking whether we should show the overlay cast button
as well as the time when the controls are auto-hiding after playback
started.

Bug:  730723 , 730838 
Change-Id: I988c07a880d05c67090ccda8665b0b54acbfa2b1
Reviewed-on: https://chromium-review.googlesource.com/527574
Commit-Queue: Anton Vayvod <avayvod@chromium.org>
Reviewed-by: Mounir Lamouri <mlamouri@chromium.org>
Cr-Commit-Position: refs/heads/master@{#478195}
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/LayoutTests/SlowTests
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/LayoutTests/media/controls/controls-cast-overlay-slow-fade.html
[add] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/LayoutTests/media/controls/controls-overlay-cast-button-autoplay-muted.html
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/LayoutTests/media/controls/controls-overlay-cast-button.html
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/LayoutTests/media/media-controls.js
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/Source/core/html/media/AutoplayPolicy.cpp
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/Source/core/html/media/AutoplayPolicy.h
[modify] https://crrev.com/e8a72f003a04193cdacbeac76d9c5cb86e15072e/third_party/WebKit/Source/modules/media_controls/MediaControlsImpl.cpp