[FR]: Use bazel_integration_test or similar to test failure cases

### What is the current behavior?

Right now, a lot of the failure cases in `examples/` are not run because they rightly fail.

### Describe the feature

It would be nice if we could assert that the tests that we expect to fail, fail. There are several ways to accomplish this, but I think [rules_bazel_integration_test](https://github.com/bazel-contrib/rules_bazel_integration_test) is the right place for this.

If we use it, we could execute tests on the `examples/*` projects from the root of the repository. I'm happy to work on the initial scaffolding if we think this is a good idea.

Start by reviewing the examples/ projects and the root repository setup, then read the rules_bazel_integration_test documentation linked in the issue. Determine how the failure cases can run from the repository root and how their expected failures should be recorded. Done means the relevant examples execute in integration tests and failures are asserted rather than skipped.

Written by the indexing model from the issue text.