feat(deep-link): posthog-code://new?prompt=… opens prefilled task input

[posthog]

Summary

Adds a new deep link key so external integrations can launch PostHog Code straight into the new-task view with an optional prompt prefilled.

URL: posthog-code://new?prompt=fix%20the%20bug (prod) or posthog-code-dev://new?prompt=… (dev).

• New "new" handler registered in TaskLinkService. The handler reads prompt from the URL's query params, treats whitespace-only values as undefined, and emits a CreateTask event (or queues it as a pending deep link if the renderer isn't ready yet).
• deepLinkRouter gets onCreateTask (subscription) + getPendingNewTaskLink (query), mirroring the existing task / inbox shape.
• useTaskDeepLink now drains pending new-task links on mount (cold start) and subscribes to onCreateTask (warm start), then calls navigateToTaskInput({ initialPrompt }) — which is the same path the codebase already uses for prefilled inputs from inbox reports.
• Window focus / restore reuses the same logic as the existing task and inbox handlers.
• 12 new unit tests in task-link/service.test.ts covering both the existing task handler (which had no tests) and the new-task handler.

Test plan

• pnpm --filter code typecheck passes
• pnpm --filter code exec vitest run src/main/services/task-link passes (12/12)
• Manually open posthog-code-dev://new?prompt=hello%20world in dev — task input opens with "hello world" prefilled
• Manually open posthog-code-dev://new — task input opens with empty prompt
• Cold start: quit the app, then open posthog-code-dev://new?prompt=test from a terminal — app launches into prefilled input

---

Created with PostHog Code