Investigate integration of Codebase Search Tool to Classic Chat ReAct vs Agentic Chat

Context

The initial Codebase Search Tool is automatically called in the Chat workflow (see gitlab.com/gitlab-org/gitlab/-/merge_requests/192086) when there is a repository or directory additional context. This does not involve any LLM inference.

As the next step, we ideally want the Codebase Search Tool to be executed with LLM support. For example, the LLM can extract the right keywords to search for based on the user's question. In order to support this, the Codebase Search Tool should be integrated in agent workflows.

The future-state architecture is Agentic Chat, while Classic Chat has the ReAct Agent.

Goals

• Figure out how to integrate the Codebase Search Tool into the new Agentic Chat
• Determine whether we should integrate the Codebase Search Tool into Classic Chat's ReAct