Enable customizing model base type to non-generated external types

[Copilot]

• Understand the problem: Models can't customize base type to non-generated types from external assemblies
• Analyze the BuildBaseModelProvider method in ModelProvider.cs
• Identify that when CustomCodeView has a base type with a namespace (external type), it needs to be looked up from Roslyn's type symbol
• Modify BuildBaseModelProvider to return null for external base types (handled by BaseTypeProvider)
• Add BuildBaseTypeProvider method to create NamedTypeSymbolProvider for external base types
• Cache external base type providers in CSharpTypeMap for future lookups
• Create comprehensive test CanCustomizeBaseModelToExternalType that validates the fix
• Run test to verify the changes work correctly
• Run broader test suite to ensure no regressions (2172 tests passed)
• Address code review feedback - add SystemObjectTypeProvider for truly external types
• Add test case for customizing base model to system type (System.Exception)
• Make test assertions more specific based on test setup
• Update test to use actual system type (System.Exception) instead of custom external type
• All 1191 generator tests pass

Original prompt

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This section details on the original issue you should resolve

<issue_title>unable to customize base type of generated model to a non-generated type</issue_title>
<issue_description>In mgmt, we have a requirement to mitigate breaking changes regarding base type of a non-generated model, such as a system object type.

public partial class KeyVaultData : Azure.ResourceManager.TrackedResourceData

The customized base type is Azure.ResourceManager.Models.TrackedResourceData, which is not generated during the current generation.

But in MTG, we have the check to ensure the custom base type is either from input model or generated model.

typespec/packages/http-client-csharp/generator/Microsoft.TypeSpec.Generator/src/Providers/ModelProvider.cs

Lines 250 to 267 in 9f01672

	// If the custom base type doesn't have a resolved namespace, then try to resolve it from the input model map.
	// This will happen if a model is customized to inherit from another generated model, but that generated model
	// was not also defined in custom code so Roslyn does not recognize it.
	if (string.IsNullOrEmpty(baseType.Namespace))
	{
	if (CodeModelGenerator.Instance.TypeFactory.InputModelTypeNameMap.TryGetValue(baseType.Name, out var baseInputModel))
	{
	baseType = CodeModelGenerator.Instance.TypeFactory.CreateCSharpType(baseInputModel);
	}
	}
	if (baseType != null && CodeModelGenerator.Instance.TypeFactory.CSharpTypeMap.TryGetValue(
	baseType,
	out var customBaseType) &&
	customBaseType is ModelProvider customBaseModel)
	{
	return customBaseModel;
	}
	}

I think the issue here is, we don't have a provider to represent such kind of type, such as InheritableSystemObjectModelProvider in mgmt.</issue_description>

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

• Fixes unable to customize base type of generated model to a non-generated type #9234

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