Add a unit test to ensure base URL with a path is handled correctly

[JamieMagee]

What are you trying to accomplish?

This is a follow-up from #13800 and #14058 to prevent a regression

Anything you want to highlight for special attention from reviewers?

How will you know you've accomplished your goal?

Checklist

• I have run the complete test suite to ensure all tests and linters pass.
• I have thoroughly tested my code changes to ensure they work as expected, including adding additional tests for new functionality.
• I have written clear and descriptive commit messages.
• I have provided a detailed description of the changes in the pull request, including the problem it addresses, how it fixes the problem, and any relevant details about the implementation.
• I have ensured that the code is well-documented and easy to understand.