Task 03: E2E — hint replaces resume button, desktop and mobile

Acceptance

apps/web/e2e/tests/settings/prevent-auto-start-on-open.spec.ts, "post-restart session does not auto-resume when the preference is on":
- after backend.restart() + testPage.reload(), asserts composer-agent-start-hint is visible and session-resume-start-button has count 0 (and "Resumed agent" never appears on its own);
- sends /e2e:simple-message via the composer (session.sendMessage) and asserts the mock response ("simple mock response") becomes visible and "Resumed agent" appears — sending a message is the explicit start.
- test.setTimeout(180_000) retained; settings/task teardown unchanged.
The two final-step tests in the same file still assert task-description-start-button visibility/absence exactly as today (CREATED button unchanged, setting-off control unchanged).
apps/web/e2e/tests/settings/mobile-prevent-auto-start-on-open.spec.ts (CREATED button on mobile) stays green unchanged.
New apps/web/e2e/tests/settings/mobile-agent-start-hint.spec.ts (mobile-chrome project, phone viewport from the project device, no per-test setViewportSize): same restart pattern — task with /e2e:simple-message description, first turn completes, backend.restart()
- testPage.reload(), then asserts composer-agent-start-hint visible, session-resume-start-button count 0, sends a message, and asserts the mock response appears. Timeouts mirror the desktop restart test (test.setTimeout(180_000)).

Verification

(cd apps/web && KANDEV_E2E_MOCK=true pnpm e2e:raw --project=chromium settings/prevent-auto-start-on-open.spec.ts)
(cd apps/web && KANDEV_E2E_MOCK=true pnpm e2e:raw --project=mobile-chrome settings/mobile-agent-start-hint.spec.ts settings/mobile-prevent-auto-start-on-open.spec.ts)

Files Likely Touched

apps/web/e2e/tests/settings/prevent-auto-start-on-open.spec.ts
apps/web/e2e/tests/settings/mobile-agent-start-hint.spec.ts (new)

Dependencies

Task 02 (the hint must be rendered before the specs can assert it).

Inputs

Current restart test body at prevent-auto-start-on-open.spec.ts:117-166 (uses backend.restart() + testPage.reload(), SessionPage.waitForLoad, session.sendMessage("/e2e:simple-message"), session.expectChatResponseVisible("simple mock response", 0, …)).
Mobile restart flow mirrors the desktop one; the mobile-chrome project auto-selects mobile-*.spec.ts files and supplies the device.

Output Contract

Desktop and mobile E2E prove: a recovered-idle session shows the composer hint and no Start agent button; sending a message starts the agent and the mock response appears; the CREATED final-step button flows (desktop and mobile) are regression-green.

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