refactor: deduplicate shared code into shared/ module

Move duplicated files from chat + batch-agent into shared/:
- shared/ws_context.py — Redis-based tool call round-trip
- shared/llm.py — LiteLLM factory (get_llm, embed)
- shared/agents/ — 4 domain agents (task, note, project, timeline)

Update all service imports to use shared.* instead of app.*.
Delete 12 duplicated files across both services.

shared/agents/timeline_agent.py

@@ -0,0 +1,116 @@
+"""Timeline agent — project milestone management (list, create, update, delete).
+
+Shared tool definitions used by both Chat and Batch Agent services.
+"""
+
+from __future__ import annotations
+
+import re
+from typing import Any
+
+from langchain_core.tools import tool
+
+from shared.ws_context import execute_on_client
+
+_UUID_RE = re.compile(
+    r"^[0-9a-fA-F]{8}-[0-9a-fA-F]{4}-[1-5][0-9a-fA-F]{3}-[89abAB][0-9a-fA-F]{3}-[0-9a-fA-F]{12}$"
+)
+
+
+def _is_uuid(value: str) -> bool:
+    return bool(_UUID_RE.match(value))
+
+TIMELINE_SYSTEM_PROMPT = (
+    "You are a project timeline assistant. Timelines are milestone dates that\n"
+    "track progress on a project — they are not calendar events.\n\n"
+    "Rules:\n"
+    "  - project_id is REQUIRED for every create; confirm with the user if unknown\n"
+    "  - For listing, project_id must be a UUID; never pass plain names as project_id\n"
+    "  - date is a Unix timestamp in milliseconds; convert human-readable dates\n"
+    "  - is_ai_suggested: 1 when proactively proposing a timeline, 0 otherwise\n"
+    "  - For update_timeline, use -1 for integer fields you do not want to change\n"
+    "  - Listing without a project_id returns all timelines across projects\n"
+    "  - Always echo the title and formatted date in your confirmation."
+)
+
+
+@tool
+async def list_timelines(project_id: str = "") -> str:
+    """List timelines. Provide project_id to scope to a specific project."""
+    normalized_project_id = project_id if (project_id and _is_uuid(project_id)) else ""
+    result = await execute_on_client(
+        action="select",
+        table="timelines",
+        filters={"projectId": normalized_project_id or None},
+    )
+    rows = result.get("rows", [])
+    if not rows:
+        return "No timelines found."
+    lines = [f"- {r['title']} (date: {r['date']}, id: {r['id']})" for r in rows]
+    return f"Found {len(rows)} timeline(s):\n" + "\n".join(lines)
+
+
+@tool
+async def create_timeline(
+    project_id: str,
+    title: str,
+    date: int,
+    is_ai_suggested: int = 0,
+) -> str:
+    """Create a project timeline (milestone).
+    project_id: REQUIRED UUID of the parent project
+    title: descriptive name for the milestone
+    date: Unix timestamp in milliseconds
+    is_ai_suggested: 1 if proactively suggested, 0 if user-requested
+    """
+    result = await execute_on_client(
+        action="insert",
+        table="timelines",
+        data={
+            "projectId": project_id,
+            "title": title,
+            "date": date,
+            "isAiSuggested": is_ai_suggested,
+        },
+    )
+    row = result["row"]
+    return f"Timeline created: '{row['title']}' (id: {row['id']}, date: {row['date']})"
+
+
+@tool
+async def update_timeline(
+    timeline_id: str,
+    title: str = "",
+    date: int = -1,
+) -> str:
+    """Update a timeline. Only pass fields that should change.
+    timeline_id: UUID of the timeline (required)
+    date: -1 means unchanged; any other value sets the new date (ms timestamp)
+    """
+    updates: dict[str, Any] = {}
+    if title:
+        updates["title"] = title
+    if date != -1:
+        updates["date"] = date
+    result = await execute_on_client(
+        action="update",
+        table="timelines",
+        data={"id": timeline_id, "updates": updates},
+    )
+    row = result["row"]
+    return f"Timeline updated: '{row['title']}' (id: {row['id']})"
+
+
+@tool
+async def delete_timeline(timeline_id: str) -> str:
+    """Delete a timeline permanently by its UUID."""
+    await execute_on_client(action="delete", table="timelines", data={"id": timeline_id})
+    return f"Timeline {timeline_id} deleted."
+
+
+TIMELINE_TOOLS: list[Any] = [
+    list_timelines,
+    create_timeline,
+    update_timeline,
+    delete_timeline,
+]