refactor(synthesis): update synthesis prompts and example output

[d-oit]

Align quality synthesis prompt templates in Python and Rust with 2026 LLM-Readable-Doc standards, update shadow skill copy, and update sample output in docs/examples/latest_synthesis.md.

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PR created automatically by Jules for task 10607628031606372805 started by @d-oit

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Project	Deployment	Actions	Updated (UTC)
do-web-doc-resolover	Ready	Preview	Aug 23, 2026 4:27am

[codacy-production]

Up to standards ✅

🟢 Issues 0 issues

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🟢 Metrics 0 complexity · 0 duplication

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