Prepare TypeScript SDK 0.1.0-beta1

[jason810496]

• related: TS SDK: replace registerTask with Dag and registerDags #71144

Why

The TypeScript SDK is ready for its first beta under the intended unscoped npm package name, with consistent release metadata and documentation. The 1.0 version remains available for a potential future migration to the @apache-airflow namespace.

What

• Rename the package and its imports from @apache-airflow/ts-sdk to apache-airflow-ts-sdk.
• Set the SDK, docs toolchain, and example versions to 0.1.0-beta1 and regenerate their lockfile metadata.
• Publish prereleases under npm's beta tag and document installing the exact beta version in SDK-owned documentation.
• Keep the Airflow core guide marked as beta while retaining its not-yet-published source-build instructions.
• Update duplicate-package diagnostics for the beta package identity.

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Was generative AI tooling used to co-author this PR?

• Yes — Codex (GPT-5)

Generated-by: Codex (GPT-5) following the guidelines

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Drafted-by: Codex (GPT-5) (no human review before posting)

[uranusjr]

Have you claimed the name yet? We should do that asap to avoid automated typosquatters. (They are probably what caused us issues; we merged the intention to use the @apache-airflow namespace first, and the commit got detected.)

[jason810496]

Have you claimed the name yet? We should do that asap to avoid automated typosquatters. (They are probably what caused us issues; we merged the intention to use the @apache-airflow namespace first, and the commit got detected.)

I just claimed it with 0.0.1-beta1 placeholder packge, thanks for the reminder. Please see https://www.npmjs.com/package/apache-airflow-ts-sdk for the live artifact.