Migrate task storage from localStorage to IndexedDB for consistency

[tyler-dane]

Priority

Medium (nice to have)

Feature Description

Currently, tasks are stored in localStorage, while events are stored in IndexedDB (see issue #1404: #1404). To improve consistency, data integrity, and align task storage with event handling, we should migrate all task storage logic from localStorage to IndexedDB.

Use Case

This migration will standardize our storage approach, reduce duplicate storage logic, and improve reliability for users accessing tasks across browser sessions or devices. IndexedDB supports more complex data structures and is already proven effective for event management.

Additional Context

• Reference: event migration in feat(web): remove auth requirement to simplify onboarding #1404
• Events are already using IndexedDB
• Consider a seamless migration for existing users so no tasks are lost
• Address backward compatibility (auto-migrate localStorage tasks on first launch after deployment)
• Technical considerations: update data-access layer, test task CRUD functionality

[linear]

COM-10