.Net: [HB Planner] Content type fix

[teresaqhoang]

Motivation and Context

Resolves #5127: If the Content-Type header of a REST API JSON response includes a charset (e.g. Content-Type: application/json; charset=utf-8), the Handlebars prompt template handles the response as a string instead of as deserialized JSON.

This PR changes the check from strict equality to a check that determine if the content type simply contains application/json

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows the SK Contribution Guidelines and the pre-submission formatting script raises no violations
• All unit tests pass, and I have added new tests where possible
• I didn't break anyone 😄