The home feed composer's action bar draws §5's bar and btn, and .composer-bar leaves the markup #4244

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 feed composer's action bar are drawn with the §5 component that fits (row, badge, bar, field or list from src/web/ui.ts and §5's classes; name which in the pull). None of .composer-bar appears in the page's HTML. The composer posts the same fields.
• [ ] Do not delete the rules from src/web/studio/feed_style.ts 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), inputs stay §5's default size, and no page-local width rule is added. A test asserts the old names are absent and the words and links are present.

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