Design: a migration's progress stages use §5's row and badge, and stage-dot/stage-detail leave §5d #3872

For: the design audit (#2678): one page at a time onto §5's components, so docs/DESIGN.md §5d only shrinks. Bringing a client's repository in shows its progress; the stages should read in plain words with §5's parts.

Done:

• [ ] A migration's progress stages (the migrate page and the browse view) is drawn from §5's components (src/web/ui.ts helpers such as row, card, badge, btn, and §5 classes) in place of .stage-dot .stage-detail, which src/web/style/content.ts defines today. src/web/client.ts selects some of these names: move its selectors to data-* attributes in the same pull, so the live behaviour is kept.
• [ ] Those classes' rules are gone, and their names leave their bullet of docs/DESIGN.md §5d. bun scripts/design-lint.ts passes, and so does --update with a lower or equal baseline.
• [ ] The pull carries before/after screenshots in light and dark, at desktop and 390 px wide. Nothing a person reads or taps is lost, and every form posts the same fields.
• [ ] The page's existing tests pass. A test asserts the old class names are absent from the page's HTML.

Files: src/web/pages/migrate.ts, src/web/pages/browse.ts, src/web/client.ts, src/web/style/content.ts, docs/DESIGN.md, the page's test. Risk: another page borrowing one of these classes. git grep each name first, and if one is used elsewhere, keep it and say so in the pull.

Parked by the crew: the check failed and the decider saw no point in another try (pull #4038 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 ("design check: nothing added outside the system (#2678) > the tree is no worse than its baseline") and the decider saw no point in another try (pull #4040 closed).

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

1. the check failed and the decider saw no point in another try (pull #4038 closed)
2. the check failed ("design check: nothing added outside the system (#2678) > the tree is no worse than its baseline") and the decider saw no point in another try (pull #4040 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 #4082, which waits for #4063 so the design check names exactly what to change; both parks were that check's baseline test.