[codex] refine startup flow

[jjoonleo]

Summary

Refines the app startup flow so launch resolves through a stable startup phase instead of bouncing between /home, sign-in, onboarding, and notification routes.

What changed

• Added an explicit auth loading state before persisted user resolution completes.
• Added a /startup screen and made it the initial route.
• Refactored router redirects into synchronous phase-based guards.
• Added a notification gate cubit with persistent Do it later handling.
• Moved notification initialization out of main.dart and into the notification gate.
• Changed onboarding intro navigation from push to go and added submit loading/error handling.
• Added the startup-flow refinement plan under plans/.

Why

The previous flow started at /home while auth was seeded as unauthenticated, so returning users could briefly see sign-in or experience route churn before the real auth state arrived. Notification permission was also checked inside router redirects, making post-sign-in and direct-home behavior inconsistent.

Validation

• dart analyze on changed files: passed
• flutter test: passed

Note: full flutter analyze still reports existing Widgetbook generated/import issues and unrelated pre-existing warnings.

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[github-actions]

Visit the preview URL for this PR (updated for commit 6a9ea14):

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