[Bug]: dotnet emitter crashes with error: "Unable to find object property with serialized name 'IndexesStatistics' in schema ListIndexStatsSummary"

### Describe the bug

Transferred from https://github.com/Azure/autorest.csharp/issues/5218

I created PR https://github.com/Azure/azure-rest-api-specs/pull/31123 to migrate Search from swagger to tsp.

The tsp project can be found at https://github.com/Azure/azure-rest-api-specs/tree/search_tsp/specification/search/Azure.Search.

The emitter crashes with error:

System.ArgumentException: An item with the same key has already been added. Key: status

https://dev.azure.com/azure-sdk/internal/_build/results?buildId=4541949&view=logs&j=2be18a23-047c-5c9f-61d7-60a33437d1f1&t=90227b5e-3523-5803-3e16-3788cf693a16&l=476

We need to identify the blockers for the search TSP migration, and this issue is preventing us from making further progress.

We would appreciate it if you could prioritize it, if possible.

Thank you!

### Reproduction

As described in the description.

### Checklist

- [x] Follow our [Code of Conduct](https://github.com/microsoft/typespec/blob/main/CODE_OF_CONDUCT.md)
- [x] Check that there isn't already an issue that request the same bug to avoid creating a duplicate.
- [x] Check that this is a concrete bug. For Q&A open a [GitHub Discussion](https://github.com/Microsoft/typespec/discussions).
- [x] The provided reproduction is a [minimal reproducible example](https://stackoverflow.com/help/minimal-reproducible-example) of the bug.