[Refactor] Extract task history persistence from ClineProvider.ts #23

Parent Issue

Part of #8 — Code Refactor on Monolith Files

Summary

Extract the task history persistence, caching, and sync cluster from src/core/webview/ClineProvider.ts into a dedicated module.

Scope

Methods to extract:

• initializeTaskHistoryStore()
• updateTaskHistory()
• scheduleGlobalStateWriteThrough()
• flushGlobalStateWriteThrough()
• broadcastTaskHistoryUpdate()
• getRecentTasks()
• getTaskWithId()
• showTaskWithId()

State owned:

• taskHistoryStore: TaskHistoryStore
• taskHistoryStoreInitialized: boolean
• recentTasksCache?: string[]
• globalStateWriteThroughTimer?: NodeJS.Timeout
• GLOBAL_STATE_WRITE_THROUGH_DEBOUNCE_MS = 5000

Estimated size: ~300–350 lines

Notes

Currently mixes caching strategy, debounced write-through, and broadcast concerns in one place. Extracting gives each a clear owner and makes the debounce/sync logic independently testable.

Constraints (from #8)

• Preserve debounce timing and write-through order
• Run type checks after extraction
• One extraction per commit