Which solution will meet these requirements with the LEAST operational overhead?

Explanations:

Creating a development stage in API Gateway allows the team to access the new version without affecting the production stage. This provides a separate environment with minimal setup, fulfilling the requirement with low operational overhead.

Creating a new API Gateway instance for beta testing would increase operational overhead, as it requires additional setup and maintenance. It also duplicates resources unnecessarily when stages are designed for this purpose.

Using a query parameter to handle versioning in the application code is not ideal. It introduces complex logic, is prone to errors, and does not leverage API Gateway’s versioning features, leading to more operational overhead.

Adding new endpoints within the same stage would not isolate beta functionality from production, potentially exposing customers to untested changes, which fails to meet the requirements.