feat: automate sponsor recognition

[rdlabo]

Summary

• Show current and past public GitHub Sponsors on the bilingual Support page
• Deduplicate sponsorship history and keep active sponsors in the current group
• Generate a static sponsor snapshot without publishing tier or payment amounts
• Refresh and deploy daily at 03:17 UTC using the GitHub Actions token
• Lazy-load the Support page and verify English and Japanese prerendered output

Privacy and failure handling

• Requests use includePrivate: false
• Generated browser data contains only login, display name, avatar URL, and GitHub profile URL
• Sponsorship amounts are used only for ordering and are removed before generation
• API failures stop the deployment, leaving the existing production site intact

Verification

• npm run fmt:check
• npm run lint
• npm test: 48 Node tests and 38 Angular tests passed
• npm run build: production build and 8 static-output tests passed
• Independent manager review: APPROVE, with no blocking or major findings

The production build still reports the configured initial bundle warning at 427.58 kB versus the 425 kB warning threshold; it remains below the 650 kB error limit.

Generated documentation

Running docs:generate also refreshed the Brother Print generated page to match its current upstream README symbol notation. This generated-only update is included so the repository generation check remains clean.