The home page's front controls and app shelf draw §5's bar and stack, and .front-controls, .app-shelf leave the markup #4291

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 front controls and the shelf that holds the app tiles are drawn with the §5 component that fits (row, bar, card, empty, filters, link or field from src/web/ui.ts and §5's classes; name which in the pull). None of .front-controls, .app-shelf appears in the page's HTML. Leave the tiles themselves (.app-tile*) to #4132 and .home-tabs to #4224.
• [ ] 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.

Parked by the crew: the check failed ("the front page > ranked, not one owner's: forks lift a stranger's app; stopped, failed and unpictured apps are not shown") and the decider saw no point in another try (pull #4305 closed). Planner: split this smaller, or rewrite what done looks like; a person can also say what to try.

Parked by the crew: the check failed ("the front page > ranked, not one owner's: forks lift a stranger's app; stopped, failed and unpictured apps are not shown") and the decider saw no point in another try (pull #4366 closed).

Parked twice since a person last spoke here, so it is the planner's now. Every reason:

1. the check failed ("the front page > ranked, not one owner's: forks lift a stranger's app; stopped, failed and unpictured apps are not shown") and the decider saw no point in another try (pull #4305 closed)
2. the check failed ("the front page > ranked, not one owner's: forks lift a stranger's app; stopped, failed and unpictured apps are not shown") and the decider saw no point in another try (pull #4366 closed)

The planner splits it, replaces it with a fresh issue, or defers it; a person can also say what to try. Nothing starts here until then, and the board lists it.

replaced by #4388: test/front.test.ts:447 finds the shelf by slicing at class="mt app-shelf", so removing the class broke the test, not the page; the new issue gives the shelf a stable hook. #4297 now waits on #4388.