Fix encode propagation for optional properties in Merge Patch

[Copilot]

Fix Encode Metadata Propagation for Merge Patch Properties

• Understand the repository structure and build system
• Analyze how encode metadata is extracted from model properties
• Identify that encode is read using getEncode(context.program, type) where type is a ModelProperty
• Discover that TypeSpec creates derived ModelProperty objects with sourceProperty when implicitOptionality is used
• Create comprehensive test cases to validate the fix (arrays, datetime, duration)
• Apply fix to check sourceProperty when encode data is not found on derived properties
• Fix applies to both array encoding and other encoding types (datetime, duration, bytes, int)
• Run tests to verify the fix works correctly
• Run code review and security checks

Original prompt

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This section details on the original issue you should resolve

<issue_title>[TCGC] encode missing for patched model</issue_title>
<issue_description>### Describe the bug

The encode metadata is not propagated or honored for optional properties when constructing the Merge Patch update model, causing emitters to generate non-encoded serialization paths for optionals.

Reproduction

TypeSpec

import "@typespec/http";
using Http;

@service(#{ title: "Array Encoding Test Service" })
namespace Encode.Array;

model Widget {
    @visibility(Lifecycle.Read)
    id: string;

    @encode(ArrayEncoding.commaDelimited)
    requiredColors: string[];

    @encode(ArrayEncoding.spaceDelimited)
    optionalColors?: string[];

}

@route("/widgets")
@tag("Widgets")
interface Widgets {
    /** Update a widget */
  @patch update(
    @path id: Widget.id,
    @body widget: MergePatchUpdate<Widget>,
  ): Widget;
}

Need to check whether encode is applied to WidgetMergePatchUpdate.optionalColors.

Checklist

• Follow our Code of Conduct
• Check that there isn't already an issue that request the same bug to avoid creating a duplicate.
• Check that this is a concrete bug. For Q&A open a GitHub Discussion.
• The provided reproduction is a minimal reproducible example of the bug.</issue_description>

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

• Fixes [TCGC] encode missing for patched model #3796

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commit: 0f5209f