GH-29309: [C++] Preserve BinaryBuilder data type

[BITree2004]

Rationale for this change

BinaryBuilder accepted a DataType in its constructor but discarded it, so finishing through ArrayBuilder::Finish() always produced a plain binary array instead of preserving the supplied type, such as an extension type backed by binary storage.

What changes are included in this PR?

• Store the supplied DataType in BaseBinaryBuilder.
• Use the stored type for BinaryBuilder and LargeBinaryBuilder output.
• Add a regression test covering BinaryBuilder with a binary-backed extension type.

Are these changes tested?

Yes.

ninja -C cpp/build arrow-array-test
./cpp/build/release/arrow-array-test --gtest_filter=BinaryBuilder.PreservesDataType
./cpp/build/release/arrow-array-test

• GitHub Issue: [C++] BinaryBuilder doesn't preserve passed in DataType #29309

[github-actions]

⚠️ GitHub issue #29309 has been automatically assigned in GitHub to PR creator.

[github-actions]

⚠️ GitHub issue #29309 has been automatically assigned in GitHub to PR creator.

[github-actions]

⚠️ GitHub issue #29309 has been automatically assigned in GitHub to PR creator.

[github-actions]

⚠️ GitHub issue #29309 has been automatically assigned in GitHub to PR creator.

[Copilot]

Pull request overview

This PR fixes BinaryBuilder / LargeBinaryBuilder so that when they’re constructed with an explicit DataType (notably binary-backed extension types), the finished array preserves that type instead of always producing a plain (large) binary array.

Changes:

• Store the provided DataType inside BaseBinaryBuilder and return it from type().
• Remove BinaryBuilder / LargeBinaryBuilder’s hardcoded type() overrides so FinishInternal() uses the stored type.
• Add a regression test ensuring a binary-backed ExtensionType is preserved through BinaryBuilder::Finish().

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 4 comments.

File	Description
cpp/src/arrow/array/builder_binary.h	Persist builder DataType in BaseBinaryBuilder and use it for finished array type.
cpp/src/arrow/array/array_binary_test.cc	Adds a regression test covering preservation of a binary-backed extension type.

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[BITree2004]

Addressed the Copilot review comments in 6ad9de9:

• validate the stored binary/large-binary builder type, including extension storage type
• use the type singleton for default binary builders
• guard typed Finish(...) overloads so extension-typed builders return TypeError instead of casting to BinaryArray/LargeBinaryArray
• add regression coverage for BinaryBuilder and LargeBinaryBuilder

Local verification:

• cmake --build cpp/build-pr-50049 --target arrow-array-test
• ./cpp/build-pr-50049/release/arrow-array-test