Add coverage for application insights

[maorleger]

Consider issues that only occur when application-insights is enabled such as:

• @azure/storage-blob and ApplicationInsights no longer working together after a dependency upgrade #20690
• Agent-based monitoring causes _a.context is not a function error #17471
• @azure/identity & @azure/keyvault-secrets latest versions throw runtime error in Azure Functions context #18260

Since we do not include applicationinsights in our smoke tests, integration tests, etc. we have missed some compatibility issues leading to costly investigations from both teams.

This leads me to believe that we will benefit from adding applicationinsights to our tests. This issue tracks investigating what would be the right approach here.

A few thoughts:

• We have a smoke test that installs all packages and runs samples or something along those lines - maybe applicationinsights should be one of the packages installed and activated?
• I think adding this as a dependency across all packages is overkill, but maybe we can consider a few select packages like storage, identity, or even core and add some happy-path tests...

[github-actions]

Hi @maorleger, we deeply appreciate your input into this project. Regrettably, this issue has remained inactive for over 2 years, leading us to the decision to close it. We've implemented this policy to maintain the relevance of our issue queue and facilitate easier navigation for new contributors. If you still believe this topic requires attention, please feel free to create a new issue, referencing this one. Thank you for your understanding and ongoing support.