The home page's apps rail draws §5's card, row and btn, and .home-rail, .home-apps, .home-app, .home-apps-verbs, .home-pick leave the markup #4269

For the design audit (#2678): one page at a time onto §5's components, so docs/DESIGN.md §5d only shrinks. Part one of two: this part changes only the markup; the stylesheet and docs/DESIGN.md are part two.

Done:

• [ ] The home page's apps rail, its app rows, their verbs and the pick control are drawn with the §5 component that fits (row, badge, bar, card, btn or field from src/web/ui.ts and §5's classes; name which in the pull). None of .home-rail, .home-apps, .home-app, .home-apps-verbs, .home-pick appears in the page's HTML. Leave .home-tabs alone: #4224 owns it.
• [ ] Do not delete the rules from the stylesheet and do not edit docs/DESIGN.md. Part two does that, and the design check stays green because the classes are still defined and named.
• [ ] Nothing a person reads or taps is lost, long unbroken text still wraps (.break), and every form posts the same fields. A test asserts the old names are absent and the words, links and forms are present.

Files: src/web/studio/home.ts, a test. Before pushing, run bun x tsc --noEmit, bun test test/design-lint.test.ts, bun scripts/design-lint.ts and the page's tests. No screenshots: the sandbox has no browser.