test(docs-infra): fix unit tests and run them for specific docs examples on CI (#36143)

Previously, only e2e tests were run for docs examples on CI. As a
result, unit tests (which are included in the zipped archives we provide
for users to download and play with the examples locally) were often
outdated and broken.

This commit configures specific docs examples that have meaningful unit
tests to run them on CI (via the `run-example-e2e.js` script). Where
necessary, the unit tests are fixed to ensure they pass and reflect the
changes in the corresponding component/service.
This commit also removes some auto-generated unit tests that are not
meaningful (e.g. make trivial assertions, such that a component instance
is truthy) and are often broken anyway (e.g. because the corresponding
component has been changed in ways that make the tests fail).

PR Close #36143

aio/tools/examples/run-example-e2e.js

@@ -9,6 +9,9 @@ const findFreePort = require('find-free-port');
 
 shelljs.set('-e');
 
+// Set `CHROME_BIN` as an environment variable for Karma to pick up in unit tests.
+process.env.CHROME_BIN = require('puppeteer').executablePath();
+
 const AIO_PATH = path.join(__dirname, '../../');
 const SHARED_PATH = path.join(__dirname, '/shared');
 const EXAMPLES_PATH = path.join(AIO_PATH, './content/examples/');