refactor: remove stale continuation semantics from Python examples

[rlippmann]

Summary

Remove stale continuation-era scaffolding and align Python examples/documentation with the current Context Compiler architecture.

This change:

• removes obsolete LiteLLM prompt-construction confirmation/session continuation code;
• removes the unused session_key flow and confirmation-token branch from the basic LiteLLM example;
• removes stale tests for the deleted confirmation helper;
• updates example-facing rejection terminology from clarify to error where the behavior represents compiler rejection rather than a human clarification workflow;
• updates documentation to describe current checkpoint, persistence, rollback, and error behavior.

Intentional checkpoint persistence and rollback behavior remain unchanged.

Why

Several examples still reflected older confirmation/continuation assumptions after the architecture moved toward explicit authoritative state transitions.

The previous terminology and helper flows implied:

• pending confirmation state;
• resumable clarification workflows;
• checkpoint-backed continuation semantics.

The current architecture distinguishes:

• compiler errors/rejected transitions;
• authoritative state persistence;
• future human-in-the-loop approval workflows.

This cleanup removes stale example behavior so the repository surface matches the current enforcement model.

Example metadata

• Enforcement point: Repository/example architecture maintenance; compiler error handling and state lifecycle clarity
• Domain: General Context Compiler examples and integrations
• Technology/runtime: Python examples, LiteLLM examples, FastAPI examples, reference integrations, documentation
• Example type: repository maintenance
• Does this use directive drafter? should normally be no: No
• Does this derive state from model output? must be no for primary examples: No

Checklist

• Repository scaffolding / governance change
• One primary enforcement point
• Explicit authoritative state
• No model-derived state mutation
• Adversarial stub or equivalent test
• Observable runtime behavior change
• Domain vocabulary is natural
• Framework is secondary to the enforcement point
• Docs updated
• Tests/smoke checks added where practical

Notes

Preserved:

• intentional checkpoint persistence examples;
• LiteLLM proxy state restoration/persistence;
• OpenWebUI transactional rollback behavior;
• compiler error handling semantics.

Removed:

• obsolete LiteLLM confirmation helper;
• unused confirmation/session continuation plumbing;
• stale documentation describing pending confirmation and resume flows.

Validation:

• ./scripts/validate_python.sh passed (204 passed, 6 skipped)
• Focused Python example test suites passed
• Markdown lint passed for updated documentation