Prerequisites

• I've searched the current open issues
• I've updated to the latest version of Toolbox

Toolbox version

0.21.0

Environment

1. OS type and version: (output of uname -a)
2. How are you running Toolbox:

• As a downloaded binary (e.g. from curl -O https://storage.googleapis.com/genai-toolbox/v$VERSION/linux/amd64/toolbox)
• As a container (e.g. from us-central1-docker.pkg.dev/database-toolbox/toolbox/toolbox:$VERSION)
• Compiled from source (include the command used to build)

Client

1. Client:
2. Version:
3. Example: If possible, please include your code of configuration:

# Code goes here! 

Expected Behavior

When executing the list_tables tool after installing AlloyDB extension in Gemini CLI, it is expected to see only tables within the user's application schema (e.g., public). Ideally, there should be a way to filter the results to exclude tables from system schema or extension-specific schema like google_ml.

Current Behavior

When I execute a query in Gemini CLI to "list tables" (which triggers the list_tables tool via the AlloyDB extension), the output includes several default tables located within the google_ml schema, in addition to the tables user have created. This clutters the output and makes it harder to focus on the application's tables.

Steps to reproduce?

1. Ensure you have an AlloyDB instance running and the Gemini CLI is installed.
2. Install the AlloyDB extension for Gemini CLI. (e.g., gemini extensions install https://github.com/gemini-cli-extensions/alloydb)
3. Configure the necessary environment variables to connect Gemini CLI to your AlloyDB instance.
4. Start Gemini CLI in interactive mode (gemini).
5. In the Gemini CLI, enter a natural language query like "List all tables" or "Show me the tables in the database."
6. Observe the output, which will include tables from the google_ml schema.

Additional Details

No response