feat: adopt checkpoint persistence and preprocessor usage in examples

[rlippmann]

Summary

Updates TS examples/docs to use current checkpoint and experimental preprocessor APIs.

Changes include:

• Node example now persists checkpoints across requests
• Node example demonstrates minimal experimental preprocessor usage
• Next.js example now persists checkpoints across requests
• Example READMEs now reflect current checkpoint/preprocessor behavior
• Examples README now reflects current transcript replay behavior

Why

Request-scoped examples should preserve pending clarification state across requests. Checkpoints are the correct persistence boundary for that.

The Node example also demonstrates a minimal experimental preprocessor flow without introducing broader host abstractions.

Scope checklist

• Diff is minimal and scoped to the requested behavior
• Python/spec parity is preserved (or mismatch is explicitly documented)
• Fixture semantics are respected (exact string vs non-empty null rule)
• No unrelated refactors
• Relevant tests were run

Notes

No core engine changes.
No fixture changes.
No CI changes.

Validation:

• npm test