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

Convert search_prompt 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 44-57)
- Update SPEC-16 checklist (16 of 16 main tools converted - prompts done!)

The search_prompt helps users search and explore their knowledge base by:
- Searching across all content in basic-memory
- Providing helpful context about search results
- Supporting optional timeframe filtering (e.g., '1d', '1 week')
- Formatting results with rich context for better understanding

This conversion maintains the prompt's search 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

@@ -463,7 +463,7 @@ Convert from `from async_client import client` to `async with get_client() as cl
 - [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`
+- [x] `prompts/search.py` (typecheck passed)
 - [ ] `resources/project_info.py`
 
 #### 0.4 Update CLI Commands (~3 files)

src/basic_memory/mcp/prompts/search.py

@@ -9,7 +9,7 @@
 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
@@ -41,16 +41,17 @@ async def search_prompt(
     """
     logger.info(f"Searching knowledge base, query: {query}, timeframe: {timeframe}")
 
-    # Create request model
-    request = SearchPromptRequest(query=query, timeframe=timeframe)
+    async with get_client() as client:
+        # Create request model
+        request = SearchPromptRequest(query=query, 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/search", json=request.model_dump(exclude_none=True)
-    )
+        # Call the prompt API endpoint
+        response = await call_post(
+            client, f"{project_url}/prompt/search", 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"]