Docs: Add real translation examples and provider onboarding

[Minseok Song (skytin1004)]

Purpose

Give first-time visitors a concrete translation result and a reproducible update/review walkthrough. Clarify that Azure is optional for Markdown and notebook translation.

Description

• Add a small two-file example, actual Korean outputs, the full translation diff, review reports, and measured run details from v0.21.0 with Azure OpenAI/gpt-5-mini.
• Show actual English and Korean GitHub screenshots from AI Agents for Beginners side by side, with original source links.
• Link the example near the top of README and the documentation homepage. Reuse the existing MkDocs theme, navigation, CLI commands, and provider configuration guide.
• Clarify OpenAI/Anthropic text support and the additional Azure AI Vision requirement for image text. Fix homepage HTML links to use built page URLs.

The walkthrough explicitly covers full-file updates, unchanged-file preservation, stale review failure, and structural review limitations. The captured Korean particle error is documented rather than silently corrected in the evidence.

• Streamline the README by consolidating repeated feature explanations and presenting the three featured repositories in a compact table. Retain setup commands, provider requirements, screenshots, and contribution links.

Related Issue

N/A

Does this introduce a breaking change?

• Yes
• No

Documentation and demo assets only; no CLI or API behavior changes.

Type of change

• Bugfix
• Feature
• Code style update (e.g., formatting, local variables)
• Refactoring (no functional or API changes)
• Documentation content changes
• Other... Please describe:

Checklist

• I have thoroughly tested my changes: strict documentation build, screenshot inspection, built image asset checks, and the previously verified provider-backed example.
• All existing tests pass: 20 focused local tests and full CI passed on the previous revision. CI for this screenshot-only update is pending; the strict documentation build passed locally.
• I have added new tests (if applicable): no production behavior changed; reused existing dry-run, onboarding, and review tests.
• I have followed the Co-op Translator coding conventions: diff whitespace check passed; no Python code is added.
• I have documented my changes (if applicable).

Additional context

Validation:

• python -m mkdocs build --strict
• python -m pytest tests/co_op_translator/test_credential_free_dry_run.py tests/co_op_translator/test_readme_onboarding_cli.py tests/co_op_translator/review/test_runner.py -q: 20 passed.
• Real CLI callbacks through Click CliRunner against the v0.21.0 wheel: initial translation/review passed; source edit produced expected stale failure; update/review passed; unchanged guide bytes and no-change rerun hashes matched.
• Initial translation: 27.36s; update: 22.17s. Setup excluded; cost not measured. These are single-run observations.

References informing presentation: PDFMathTranslate (result-first entry), Lingo.dev and Repomix (clear positioning and try-it links). No claim of causal impact on stars.

Proposed companion GitHub About setting (not changed by this PR):

Keep repository translations up to date. Translate Markdown and notebooks with Azure OpenAI, OpenAI, or Anthropic; image text with Azure AI Vision.

Suggested additional topics: documentation, translation, i18n, openai, anthropic, jupyter-notebook, mcp. Repository settings remain unchanged for this draft.