refactor(app): integrate chat store SRP chain

[Andiveli]

Summary

• Separate hydration, message storage, receipts, read-state policy, and cursor restoration.
• Integrate the completed, independently verified SRP chain into beta.

Changes

• refactor(app): extract chat store hydration #363 hydration\n- refactor(chat-store): extract message storage responsibility #367 message storage\n- refactor(chat-store): extract receipt coordination #368 receipt coordination\n- refactor(chat-store): extract read-state policy #369 read-state policy\n- refactor(chat-store): delegate cursor restoration to read state #370 cursor restoration

Testing

• Every child PR passed its required CI before merge
• Every child remained within the 400-line review budget
• Tracker branch contains only the ordered chain
• Integration PR CI pending

Chain Context

beta
└── 📍 refactor/chat-store-srp

Start: beta at cd65022.
End: the complete SRP chain is available on beta.
Out of scope: main, release, and unrelated feature work.

Closes #361