Enable some more passing browser tests with network service.

Bug: 797292, 859594

Cq-Include-Trybots: luci.chromium.try:linux_mojo
Change-Id: Id4e90f0ebdf5ac172b12c92d80b54348125bc883
Reviewed-on: https://chromium-review.googlesource.com/1171556Reviewed-by: Chris Mumford <cmumford@chromium.org>
Commit-Queue: John Abd-El-Malek <jam@chromium.org>
Cr-Commit-Position: refs/heads/master@{#582328}

testing/buildbot/filters/mojo.fyi.network_browser_tests.filter

@@ -8,9 +8,7 @@
 # Uncategorized timeouts or test failures.
 -ExtensionDisabledGlobalErrorTest.HigherPermissionsFromSync
 -ExtensionDisabledGlobalErrorTest.RemoteInstall
--ExtensionStorageMonitorTest.HostedAppTemporaryFilesystem
 -ExtensionUnloadBrowserTest.UnloadWithContentScripts
--ProcessManagerBrowserTest.NestedURLNavigationsToExtensionAllowed
 -ProxySettingsApiTest.ProxyEventsInvalidProxy
 -RegisterProtocolHandlerBrowserTest.CustomHandler
 -SubresourceFilterBrowserTest.FailedProvisionalLoadInMainframe
@@ -113,9 +111,6 @@
 -DnsProbeBrowserTest.CorrectionsLoadStopped
 -DnsProbeBrowserTest.NoInternetProbeResultWithSlowBrokenCorrections
 
-# crbug.com/859594 Migrate storage::FileWriterDelegate to use SimpleURLLoader
--SBNavigationObserverBrowserTest.DownloadViaHTML5FileApi
-
 # https://bugs.chromium.org/p/chromium/issues/detail?id=789670
 -DiceBrowserTest.Reauth
 -DiceBrowserTest.Signin
@@ -184,10 +179,6 @@
 # Remove this test when there are no more clients left that use URLFetcher.
 -VariationsHttpHeadersBrowserTest.TestStrippingHeadersFromInternalRequest
 
-# Fails because of missing support to navigate to filesystem: URLs.
-# https://crbug.com/797292
--ProcessManagerBrowserTest.NestedURLDownloadsToExtensionAllowed
-
 # Tests check state of NQE in the browser process, but need to be updated to
 # watch NQE in the renderer process.
 # https://crbug.com/819244