Add backward compatibility support for constructor accessibility on abstract base types

[Copilot]

Problem

Regenerating SDKs from TypeSpec (previously from autorest) changes constructor accessibility on abstract base types, breaking existing code. Example from Azure.Search.Documents:

Previous (autorest):

public abstract partial class SearchIndexerDataIdentity
{
    public SearchIndexerDataIdentity() { }
}

Current (TypeSpec without fix):

public abstract partial class SearchIndexerDataIdentity
{
    private protected SearchIndexerDataIdentity(string odataType) { }
    // Constructor is private protected instead of public
}

Changes

Core Implementation

• TypeProvider.ProcessTypeForBackCompatibility: Extended to process constructors in addition to methods
• TypeProvider.BuildConstructorsForBackCompatibility: New virtual method for constructor backward compatibility logic
• ModelProvider.BuildConstructorsForBackCompatibility: Changes constructor modifiers from private protected to public on abstract base types when the last contract had a public constructor with matching parameters

Approach

This implementation changes the accessibility modifier on existing constructors rather than generating new ones. It only applies when:

1. The type is an abstract base type
2. The last contract had a public constructor
3. The current version generates a private protected constructor with matching parameters (same count, types, and names)

Generated Code

public abstract partial class SearchIndexerDataIdentity
{
    /// <summary> Initializes a new instance of SearchIndexerDataIdentity. </summary>
    public SearchIndexerDataIdentity(string odataType) 
    {
        OdataType = odataType;
    }
}

Testing

• Added BackCompat_AbstractTypeConstructorAccessibility test that verifies constructor modifiers change from private protected to public
• All 1231 tests pass
• Updated documentation with new "Model Constructors" section

Original prompt

---

This section details on the original issue you should resolve

<issue_title>[Bug]: Backward Compatibility not generating pre-existing public constructors</issue_title>
<issue_description>### Describe the bug

Pre-existing public constructors should not be missing from the generated code. This should be another Back Compat scenario. See Backward Compatibility Support for more details.

Generating Azure.Search.Documents have the issue where a public constructor is missing, for instance, this is what the previously generated code from autorest looks like:

// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.

// <auto-generated/>

#nullable disable

using System;
using System.Collections.Generic;

namespace Azure.Search.Documents.Indexes.Models
{
    /// <summary>
    /// Abstract base type for data identities.
    /// Please note <see cref="SearchIndexerDataIdentity"/> is the base class. According to the scenario, a derived class of the base class might need to be assigned here, or this property needs to be casted to one of the possible derived classes.
    /// The available derived classes include <see cref="SearchIndexerDataNoneIdentity"/> and <see cref="SearchIndexerDataUserAssignedIdentity"/>.
    /// </summary>
    public abstract partial class SearchIndexerDataIdentity
    {
        /// <summary>
        /// Keeps track of any properties unknown to the library.
        /// <para>
        /// To assign an object to the value of this property use <see cref="BinaryData.FromObjectAsJson{T}(T, System.Text.Json.JsonSerializerOptions?)"/>.
        /// </para>
        /// <para>
        /// To assign an already formatted json string to this property use <see cref="BinaryData.FromString(string)"/>.
        /// </para>
        /// <para>
        /// Examples:
        /// <list type="bullet">
        /// <item>
        /// <term>BinaryData.FromObjectAsJson("foo")</term>
        /// <description>Creates a payload of "foo".</description>
        /// </item>
        /// <item>
        /// <term>BinaryData.FromString("\"foo\"")</term>
        /// <description>Creates a payload of "foo".</description>
        /// </item>
        /// <item>
        /// <term>BinaryData.FromObjectAsJson(new { key = "value" })</term>
        /// <description>Creates a payload of { "key": "value" }.</description>
        /// </item>
        /// <item>
        /// <term>BinaryData.FromString("{\"key\": \"value\"}")</term>
        /// <description>Creates a payload of { "key": "value" }.</description>
        /// </item>
        /// </list>
        /// </para>
        /// </summary>
        private protected IDictionary<string, BinaryData> _serializedAdditionalRawData;

        /// <summary> Initializes a new instance of <see cref="SearchIndexerDataIdentity"/>. </summary>
        public SearchIndexerDataIdentity()
        {
        }

        /// <summary> Initializes a new instance of <see cref="SearchIndexerDataIdentity"/>. </summary>
        /// <param name="oDataType"> A URI fragment specifying the type of identity. </param>
        /// <param name="serializedAdditionalRawData"> Keeps track of any properties unknown to the library. </param>
        internal SearchIndexerDataIdentity(string oDataType, IDictionary<string, BinaryData> serializedAdditionalRawData)
        {
            ODataType = oDataType;
            _serializedAdditionalRawData = serializedAdditionalRawData;
        }

        /// <summary> A URI fragment specifying the type of identity. </summary>
        internal string ODataType { get; set; }
    }
}

and the new generated model looks like:

// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.

// <auto-generated/>

#nullable disable

using System;
using System.Collections.Generic;

namespace Azure.Search.Documents.Models
{
    /// <summary>
    /// Abstract base type for data identities.
    /// Please note this is the abstract base class. The derived classes available for instantiation are: <see cref="SearchIndexerDataNoneIdentity"/> and <see cref="SearchIndexerDataUserAssignedIdentity"/>.
    /// </summary>
    public abstract partial class SearchIndexerDataIdentity
    {
        /// <summary> Keeps track of any properties unknown to the library. </summary>
        private protected readonly IDictionary<string, BinaryData> _additionalBinaryDataProperties;

        /// <summary> Initializes a new instance of <see cref="SearchIndexerDataIdentity"/>. </summary>
        /// <param name="odataType"> A URI fragment specifying the type of identity. </param>
        private protected SearchIndexerDataIdentity(string odataType)
        {
            OdataType = odataType;
        }

        /// <summary> Initializes a new instance of <see cref="SearchIndexerDataIdentity"/>. </summary>
  ...

</details>



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- Fixes microsoft/typespec#9483

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[github-actions]

No changes needing a change description found.

[JoshLove-msft]

Fixes #9483