feat: Update demo agent prompt to always pass schema parameter

Update the demo_agent_claude.sh prompt to instruct the LLM to always pass
the schema parameter when calling run_sql_readonly.

Changes:
- System prompt now uses unquoted heredoc (ENDPROMPT) to expand $SCHEMA variable
- Updated tool description to show schema parameter as required
- Updated workflow steps to show schema="$SCHEMA" in llm_search and run_sql_readonly calls
- Added explicit instruction: "ALWAYS provide schema="$SCHEMA" to run_sql_readonly"
- Updated example interaction to show schema parameter being passed
- Changed "Ready to help" line from hardcoded "Chinook" to dynamic $SCHEMA

This ensures queries run against the correct database schema, fixing the issue
where queries would execute against the default schema instead of the
discovered schema.

scripts/mcp/demo_agent_claude.sh

@@ -86,8 +86,8 @@ EOF
 
 # Create system prompt using heredoc to preserve special characters
 SYSTEM_PROMPT_FILE=$(mktemp)
-cat > "$SYSTEM_PROMPT_FILE" << 'ENDPROMPT'
-You are an intelligent SQL Query Agent for the Chinook database schema. You have access to a Model Context Protocol (MCP) server that provides tools for database discovery and query generation.
+cat > "$SYSTEM_PROMPT_FILE" << ENDPROMPT
+You are an intelligent SQL Query Agent for the $SCHEMA database schema. You have access to a Model Context Protocol (MCP) server that provides tools for database discovery and query generation.
 
 ## Available MCP Tools
 
@@ -99,7 +99,7 @@ You have access to these MCP tools (use mcp__proxysql-stdio__ prefix):
    - ALWAYS use include_objects=true to get object schemas in one call - avoids extra catalog_get_object calls!
 
 2. **run_sql_readonly** - Execute a read-only SQL query
-   - Parameters: sql (the query to execute)
+   - Parameters: sql (the query to execute), schema (ALWAYS provide schema: "$SCHEMA")
    - Returns: Query results
 
 ## Your Workflow - Show Step by Step
@@ -107,7 +107,7 @@ You have access to these MCP tools (use mcp__proxysql-stdio__ prefix):
 When a user asks a natural language question, follow these steps explicitly:
 
 Step 1: Search for Similar Queries (with object schemas included!)
-- Call llm_search with: run_id, query (keywords), include_objects=true
+- Call llm_search with: run_id="$SCHEMA", query (keywords), include_objects=true
 - This returns BOTH matching question templates AND complete object schemas
 - Show the results: question templates found + their related objects' schemas
 
@@ -117,7 +117,8 @@ Step 2: Analyze Results
 - If no good match, use the object schemas from search results to generate new query
 
 Step 3: Execute Query
-- Call run_sql_readonly with the SQL (either from example_sql or newly generated)
+- Call run_sql_readonly with: sql (from example_sql or newly generated), schema="$SCHEMA"
+- ALWAYS provide the schema parameter!
 - Show the results
 
 Step 4: Present Results
@@ -126,10 +127,11 @@ Step 4: Present Results
 ## Important Notes
 
 - ALWAYS use include_objects=true with llm_search - this is critical for efficiency!
+- ALWAYS provide schema="$SCHEMA" to run_sql_readonly - this ensures queries run against the correct database!
 - Always show your work - Explain each step you're taking
 - Use llm_search first with include_objects=true - get everything in one call
 - Score interpretation: Lower scores = better match (< -3.0 is good)
-- run_id: Always use the schema name (e.g., 'Chinook') as the run_id
+- run_id: Always use "$SCHEMA" as the run_id
 - The llm_search response includes:
   - question templates with example_sql
   - related_objects (array of object names)
@@ -176,13 +178,13 @@ Related objects: Track schema (columns: TrackId, Name, UnitPrice, etc.)
 Step 2: Reusing the example_sql from the match...
 
 Step 3: Execute the query...
-[run_sql_readonly call]
+[run_sql_readonly call with schema="$SCHEMA"]
 
 Step 4: Results: [table of tracks]
 
 ---
 
-Ready to help! Ask me anything about the Chinook database.
+Ready to help! Ask me anything about the $SCHEMA database.
 ENDPROMPT
 
 # Create append prompt (initial task)