refactor(mcp): convert continue_conversation.py to context manager pattern

Convert continue_conversation MCP prompt from module-level client import to
the new get_client() context manager pattern, enabling proper dependency injection.

Changes:
- Import get_client() instead of client from async_client module
- Wrap function body in 'async with get_client() as client:' block
- Indent all code inside context manager (lines 45-62)
- Update SPEC-16 checklist (15 of 16 main tools converted)

The continue_conversation prompt helps users continue conversations and work
across sessions by:
- Finding recent context about specific topics
- Showing general recent activity with timeframe filtering
- Providing context from previous sessions to maintain continuity
- Supporting session continuation in MCP-enabled AI assistants

This conversion maintains the prompt's session continuation functionality while:
- Ensuring proper client lifecycle management
- Enabling cloud app to inject custom transport via factory
- Allowing tests to mock client behavior
- Following httpx best practices for async context managers
- Moving auth to client creation instead of per-request

Testing:
- Typecheck passed (0 errors, 0 warnings)
- Prompt function properly scoped (client inside async with block)

Part of Phase 0.3: Converting 16 MCP tools/prompts to context manager pattern.
Related to SPEC-16 MCP Cloud Service Consolidation.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: phernandez

specs/SPEC-16 MCP Cloud Service Consolidation.md

@@ -462,8 +462,8 @@ Convert from `from async_client import client` to `async with get_client() as cl
 - [x] `tools/canvas.py` (5/5 tests passing)
 - [x] `tools/build_context.py` (6/6 tests passing)
 - [x] `tools/sync_status.py` (typecheck passed)
+- [x] `prompts/continue_conversation.py` (typecheck passed)
 - [ ] `prompts/search.py`
-- [ ] `prompts/continue_conversation.py`
 - [ ] `resources/project_info.py`
 
 #### 0.4 Update CLI Commands (~3 files)

src/basic_memory/mcp/prompts/continue_conversation.py

@@ -10,7 +10,7 @@
 from pydantic import Field
 
 from basic_memory.config import get_project_config
-from basic_memory.mcp.async_client import client
+from basic_memory.mcp.async_client import get_client
 from basic_memory.mcp.server import mcp
 from basic_memory.mcp.tools.utils import call_post
 from basic_memory.schemas.base import TimeFrame
@@ -42,20 +42,21 @@ async def continue_conversation(
     """
     logger.info(f"Continuing session, topic: {topic}, timeframe: {timeframe}")
 
-    # Create request model
-    request = ContinueConversationRequest(  # pyright: ignore [reportCallIssue]
-        topic=topic, timeframe=timeframe
-    )
+    async with get_client() as client:
+        # Create request model
+        request = ContinueConversationRequest(  # pyright: ignore [reportCallIssue]
+            topic=topic, timeframe=timeframe
+        )
 
-    project_url = get_project_config().project_url
+        project_url = get_project_config().project_url
 
-    # Call the prompt API endpoint
-    response = await call_post(
-        client,
-        f"{project_url}/prompt/continue-conversation",
-        json=request.model_dump(exclude_none=True),
-    )
+        # Call the prompt API endpoint
+        response = await call_post(
+            client,
+            f"{project_url}/prompt/continue-conversation",
+            json=request.model_dump(exclude_none=True),
+        )
 
-    # Extract the rendered prompt from the response
-    result = response.json()
-    return result["prompt"]
+        # Extract the rendered prompt from the response
+        result = response.json()
+        return result["prompt"]