Search across all your workspaces in one place

• Cross-workspace search from your AI assistant: Search by name or title across all accessible workspaces, with paginated results and disambiguation metadata.
• Default workspace on create: Creating a conversation no longer requires specifying a workspace; it defaults to your primary one. Responses now include workspace info.
• Workspace context in responses: Create, respond, and update responses consistently include workspace ID and name.

• Clearer search behavior: List endpoints handle browse and search, with detailed lookup reserved for fetching by ID.
• Embed options panel reordered: preview and embed code first, appearance options at the bottom.

Correct access control in search: Visibility checks now use the actual visibility list, ensuring users only see researches they're permitted to.