refactor: Route async task mode through TaskExecutionService (#95)

[AndriiPasternak31]

Summary

• Replaced inline slot/activity/sanitization/error logic in _execute_task_background() with delegation to TaskExecutionService, matching the pattern used by internal.py and public.py
• Extracted _save_to_chat_session() helper to eliminate DRY violation between async and sync session persistence paths
• Net reduction of ~124 lines in chat.py

Changes

• src/backend/routers/chat.py — Rewrote _execute_task_background() as thin wrapper, simplified async branch, extracted shared helper
• tests/test_parallel_task.py — Added 5 new tests (session persistence, collaboration activity, safety net)
• docs/memory/changelog.md — Added changelog entry
• docs/memory/feature-flows/task-execution-service.md — Updated flow documentation

Test Plan

• Existing tests pass: pytest tests/test_parallel_task.py -v
• New tests pass: TestAsyncSessionPersistence, TestAsyncCollaborationActivity, TestAsyncSafetyNet
• Manual: async task returns immediately and completes via polling
• Manual: sync task with save_to_session still persists to chat session
• Manual: agent-to-agent async task completes collaboration activity

Closes #95

Generated with Claude Code

[vybe]

Thanks for the clean refactor! The delegation pattern is solid and the 5 new tests are a great addition. A few items before merge:

Required

• execution_time_ms regression in _save_to_chat_session() — The old _execute_task_background() passed execution_time_ms to db.add_chat_message(). The new helper omits it because TaskExecutionResult has no such field. Async chat sessions will now always store NULL for execution time. Either add execution_time_ms: Optional[int] to TaskExecutionResult and populate it in the service, or explicitly accept this loss and document it.

• context_used guard dropped — Old: context_used if context_used > 0 else None. New: stores result.context_used directly (could persist 0 instead of NULL). Small behavior change worth preserving for consistency.

• Please rebase onto main before merge — the branch has a merge commit (merge: resolve changelog conflict with upstream/main) that should be cleaned up.

Minor

• Issue #95 is missing the type-refactor label.
• Confirm public.py's _execute_public_chat_background() (line 775) is considered resolved — it appears to already delegate to TaskExecutionService, but the issue's "Files to Change" section lists it. Either close the loop in the PR description or follow up in a separate issue.
• Add ## Security Considerations section to task-execution-service.md (even a brief "N/A — service layer, no direct auth or user input" is sufficient to satisfy the flow format spec).

Please address the required items and request re-review.