Playwright 375px smoke for public landing and /demo

## Task

#9 covers dashboard hub nav. Public `/` and `/demo` have no mobile viewport smoke.

## Scope

- Add or extend tests under `tests/browser/`
- Viewport 375×667
- Assert Start talking, Run trust loop, and Run one-click sample call are visible/clickable without horizontal overflow on `/demo`
- Assert landing primary CTAs are visible

## Acceptance criteria

- [ ] `make test-browser` passes locally and in CI
- [ ] Does not replace #9
- [ ] No screenshot goldens unless the suite already uses them

Start by inspecting the existing browser tests under tests/browser/ and run make test-browser. Add 375×667 coverage for / and /demo, checking the named CTAs are visible and clickable without horizontal overflow. Done means the browser suite passes locally and in CI without replacing #9 or adding screenshot goldens unless the suite already uses them.

Written by the indexing model from the issue text.