refactor(app): split chat store responsibilities

[Andiveli]

Problem

src/app/chat_store.rs currently combines database hydration/contact synchronization, message/chat storage projection, and read/status cursor policy in one App implementation.

Requested outcome

Extract cohesive internal responsibility modules while preserving the existing App APIs and behavior.

Scope

• Separate database hydration and contact synchronization.
• Separate message/chat storage and projection updates.
• Separate read/status cursor and receipt policy.
• Keep characterization tests with each responsibility.

Out of scope

No user-visible behavior, schema, public API, or dependency changes.

Verification

Run the focused Rust tests, the single-threaded Rust suite, formatting, and diff checks for each reviewable chain slice.