What's left to do here? 

Let me write a test that uses FDS to add team drives and entries, and then we'll know it works for sure. I'll close this bug after that.

FWIW We already have those, unless you're talking about some JS tests.

Talking about JS tests, yes.

This is done, as of https://chromium-review.googlesource.com/c/chromium/src/+/1117719. :)

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/f721bbdf94479979077874ff12000e39c8d40d5a

commit f721bbdf94479979077874ff12000e39c8d40d5a
Author: Sasha Morrissey <sashab@chromium.org>
Date: Mon Jul 09 03:51:05 2018

Add support for capabilities in Team Drive tests

Add support for capabilities in Team Drive tests, including a unit test
for the new method in FakeDriveService and a browser test that
transfers files between Drive, Downloads and Team Drives.

Bug: 719959, 846561 
Cq-Include-Trybots: luci.chromium.try:closure_compilation
Change-Id: I3935ab56cf481f3fc5e61beb12e966d21223b155
Reviewed-on: https://chromium-review.googlesource.com/1124066
Commit-Queue: Sasha Morrissey <sashab@chromium.org>
Reviewed-by: Luciano Pacheco <lucmult@chromium.org>
Cr-Commit-Position: refs/heads/master@{#573208}
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/chrome/browser/chromeos/file_manager/file_manager_browsertest.cc
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/chrome/browser/chromeos/file_manager/file_manager_browsertest_base.cc
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/components/drive/service/fake_drive_service.cc
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/components/drive/service/fake_drive_service.h
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/components/drive/service/fake_drive_service_unittest.cc
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/ui/file_manager/file_manager/background/js/test_util.js
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/ui/file_manager/file_manager/foreground/js/file_transfer_controller.js
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/ui/file_manager/integration_tests/file_manager/context_menu.js
[modify] https://crrev.com/f721bbdf94479979077874ff12000e39c8d40d5a/ui/file_manager/integration_tests/file_manager/transfer.js