Implement the Sidebar

This issue is good to work once #43 has been implemented

- [x] User should be able to see list of Chats by docs
- [ ] Filter Chats by docs type (By a dropdown menu)
- [x] User should have a button in sidebar to create a new Chat
- [ ] On a New Chat Page User should have a option to select the AI agent they want to choose for the conversation
AI Agent: refers to the documentation bot for the conversation (flutter, nextjs)
- [ ] Once a AI agent is choosen for a conversation it cannot be changed in the middle of the conversation, User must create a new chat for a new agent

Start by verifying that issue #43 is implemented, then inspect the existing sidebar and New Chat page entry points. Confirm how chats are listed and how documentation types and AI agents are represented. Done means users can filter chats, create a chat, select an agent only when starting a chat, and cannot change that agent during the conversation.

Written by the indexing model from the issue text.