[Refactor] Extract ClineMessagesStore from Task.ts #17

Parent Issue

Part of #8 — Code Refactor on Monolith Files

Summary

Extract the UI chat message persistence cluster from src/core/task/Task.ts into a dedicated ClineMessagesStore module.

Scope

Methods to extract:

• getSavedClineMessages()
• addToClineMessages()
• overwriteClineMessages()
• updateClineMessage()
• saveClineMessages()
• findMessageByTimestamp()

State owned:

• clineMessages: ClineMessage[]
• cloudSyncedMessageTimestamps: Set<number>
• lastMessageTs?: number

Estimated size: ~200–250 lines

Notes

This is a symmetric pattern to the already-extracted apiConversationHistory module, making it a low-risk, straightforward extraction. Task.ts becomes a thin consumer of both stores.

Constraints (from #8)

• Preserve method names and call signatures
• Maintain event emission and side-effect order
• Run type checks after extraction
• One extraction per commit