docs: make the first run work from the README

[Adeniyikayodee]

Documentation only, plus one test stub and one line in the doc generator. No library code or package name changes.

• Python README and site: the lookup example uses a code the API reports as assigned, handles the error cases, and explains levels and where to get a key.
• Root README: offline examples come first, a "Start here" table routes a task to a package, and a note covers the two names people get wrong.
• Root, Python, and crate READMEs: one table says which form to store, show, and exchange.
• The live API differences move to docs/api-differences.md as one dated table, linked from the README, CONTRIBUTING.md, and llms.txt.

Tested: Python, MCP, resolver, and Rust suites, and scripts/llms_full.py --check.