[webview_flutter] Remove duplicate integration test

[stuartmorgan-g]

This test is for a change that was entirely in Android Java code when it
was written, so is testing behavior that is internal to the Android
implementation, and a copy of this test already runs
webview_flutter_android. Given that it's testing internal Android
behavior, only that copy is needed.

For unknown reasons, this copy seems to hang test runs, while the
webview_flutter_android copy does not. Since it's a duplicate that we
want to remove anyway, this simply removes it to fix the tree without
meaningful loss of coverage.

Also fixes a race condition in an integration test, where a future
could be completed more than once.

Part of flutter/flutter#91004

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read and followed the relevant style guides and ran the auto-formatter. (Unlike the flutter/flutter repo, the flutter/plugins repo does use dart format.)
• I signed the CLA.
• The title of the PR starts with the name of the plugin surrounded by square brackets, e.g. [shared_preferences]
• I listed at least one issue that this PR fixes in the description above.
• I updated pubspec.yaml with an appropriate new version according to the pub versioning philosophy, or this PR is exempt from version changes.
• I updated CHANGELOG.md to add a description of the change, following repository CHANGELOG style.
• I updated/added relevant documentation (doc comments with ///).
• I added new tests to check the change I am making, or this PR is test-exempt.
• All existing and new tests are passing.

[stuartmorgan-g]

This fixes things for me locally, but doesn't seem to be enough to make CI happy :(

[stuartmorgan-g]

I'm going to go ahead and land this even though it's not enough to fix CI since it does at least fix issues I'm having locally, so landing it should remove some potential issues for people trying to reproduce the problem locally to figure out a fix.