A search hit in an archived repository wears an `Archived` badge, on the page and in MCP `search` #6084

An archived repository stays searchable, which is right, but src/web/pages/search.ts marks only Private, so a hit from something put away reads as live.

Done when:

• [ ] Next to the existing private badge (search.ts privateBadge), a repository or code hit from an archived repository shows a secondary Archived badge, using §5's badge.
• [ ] MCP search rows carry archived: true|false.
• [ ] A test archives a repository, searches for its name, and finds the badge and the flag. bun scripts/design-lint.ts passes.