Rename XML model serialization helper method from Write to WriteXml

[Copilot]

The private Write(XmlWriter, ModelReaderWriterOptions, string) helper method in XML model serialization collides with model properties named Write (e.g., Azure Storage's BlobAnalyticsLogging.Write), causing compile errors in generated code.

Changes

• Core rename: XmlWriteMethodName constant changed from "Write" to "WriteXml" in MrwSerializationTypeDefinition.Xml.cs
• Test filters updated: MockMrwProvider and FilteredMethodsTypeProvider lambdas in XmlSerializationTests.cs updated to match both "WriteXml" (private helper) and "Write" (the IPersistableModel<T>.Write explicit interface method)
• Test data files: All expected output files updated with the new private helper method name WriteXml; the IPersistableModel<T>.Write explicit interface method is preserved unchanged
• Generated files: Sample-TypeSpec generated serialization files updated to reflect the rename

Before / After

// Before — collides with model properties named "Write"
private void Write(XmlWriter writer, ModelReaderWriterOptions options, string nameHint) { ... }

// After
private void WriteXml(XmlWriter writer, ModelReaderWriterOptions options, string nameHint) { ... }

Original prompt

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This section details on the original issue you should resolve

<issue_title>Rename Write Method in XML Model Serialization</issue_title>
<issue_description>The Write method name is too generic and it already is leading to a collision in Storage with one of the model's properties.</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Rename Write Method in XML Model Serialization #9748

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