[C#][Integration] Integration CI job is still failing for C# consumers

### Describe the bug, including details regarding any error messages, version, and platform.

Sorry for the spam with these...I didn't check the full integration CI job before merging https://github.com/apache/arrow/pull/41259 😬 . PR incoming! There are still issues:

https://github.com/apache/arrow/actions/runs/8725386715/job/23938224643

### Component(s)

C#, Integration