[Feature Request] Support organizing conversations into Projects / Folders (similar to Claude / ChatGPT Projects)

Feature Description

Add the ability for users to organize conversations into custom projects or folders in the sidebar, rather than relying solely on the standard chronological list (e.g., "Today", "Previous 7 Days").

Problem / Motivation

As users rely on HuggingChat across distinct workflows (e.g., coding, research, writing, personal projects), the current chronological sidebar makes it difficult to manage ongoing work. Important conversations get buried quickly as new chats are generated.

Proposed Solution

• Project / Folder Structure (Primary Goal):

  • Allow users to create custom folders/projects in the sidebar.
  • Provide a simple way (drag-and-drop or a "Move to Project" menu option) to assign chats to specific folders.
  • Keep unassigned chats in the default chronological view, while project chats are grouped under collapsible folders.

• Project-Level Context & Instructions (Stretch Goal / Future Enhancement):

  • Inspired by platforms like Claude Projects, ChatGPT Projects, or Gemini Notebooks, allow projects to optionally hold custom system instructions or context files shared across all chats within that project.

Comparison & Inspiration

Other major AI assistants (Claude, ChatGPT, Gemini) have moved toward project/notebook-based organization to support long-term, multi-chat workflows. Implementing even a basic folder-based grouping system in chat-ui would significantly improve workspace management for power users.