The origins page's handoff and connect path draw §5's card, row and btn, and .handoff, .handoff-links, .connect-more, .connect-path leave the markup #4154

Part one of #3839, which went red as one change. This part changes only the markup; the stylesheet and docs/DESIGN.md are part two.

Done:

• [ ] The origins page's handoff and connect steps are drawn with §5's card, row and btn from src/web/ui.ts and §5's classes. None of .handoff .handoff-links .connect-more .connect-path appears in the page's HTML.
• [ ] Do not delete the rules from src/web/style/content.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, 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/pages/origins.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.