The passkey state on the site, claim and first-admin pages draws §5's badge and stack, and no class="passkey…" remains in the markup #4698

Done:

• [ ] src/web/pages/site.ts, claim.ts and first-admin.ts draw the passkey on/off state as §5's badge() (success when on) inside base.ts stack utilities; no class="passkey in src/web/pages/.
• [ ] A test fetches each page and asserts the state word and no passkey-on.

Markup only: the stylesheet and docs/DESIGN.md are not touched in this pull (their rules leave in a follow-up), so it cannot conflict with the many pulls editing src/web/style/content.ts. Run bun x tsc --noEmit, bun scripts/design-lint.ts and bun test test/design-lint.test.ts before pushing; where counts fall, lower docs/design/baseline.json in the same pull.