Design: the front page's admin controls draw §5's row, bar and field, and front-admin/pick/pin-any/weights leave §5d #4085

Replaces #3941 (parked twice on the design check's baseline). Waits for #4063, and for the featured-app change so two pulls do not edit home.ts at once.

Done:

• [ ] frontControls in src/web/studio/home.ts is drawn from row, .bar, field and btn, and posts the same fields to /front.
• [ ] .front-admin, .front-pick, .front-pin-any, .front-weights leave src/web/style/content.ts and §5d.
• [ ] A test asserts the old names are absent and each form posts the same field names; the home tests and bun x tsc --noEmit pass.

Before you push, run bun test test/design-lint.test.ts and bun scripts/design-lint.ts: every line they print names the file and what to change; fix each one. Striking a class from docs/DESIGN.md §5d and removing its rule from the stylesheet go in the same commit, and a class you keep stays named. Rebase onto main right before pushing: docs/DESIGN.md changes under everyone.

Files: src/web/studio/home.ts, src/web/style/content.ts, docs/DESIGN.md, docs/design/baseline.json, a test.