Feature request: shared context between Claude Code, Claude.ai and Cowork

Problem

Claude's product suite (Claude Code CLI, Claude.ai web, Cowork, mobile apps) currently operates as isolated silos. There is no shared context between them, which creates friction for users who work across these tools.

Concrete example: I built a /transacties skill in Claude Code that updates a local SQLite database via MCP servers and Python scripts. When I tried to use this skill in Cowork, Claude responded: "I don't have access to MCP or those scripts." The skill, memory files, and MCP connections — none of it carries over.

What doesn't transfer between Claude products today

• Skills / custom commands — only available in Claude Code
• Memory files (.claude/ project memory) — not accessible from Claude.ai/Cowork
• MCP server connections — CLI only
• Conversation context — no continuity between Code and Cowork
• CLAUDE.md project instructions — ignored outside Code

Suggestion

Consider a shared layer where at minimum:

1. Project memory and skills are accessible across Claude Code, Cowork, and Claude.ai Projects
2. MCP servers can be registered once and used from any Claude surface (perhaps via a persistent daemon or cloud relay)
3. Context handoff between Claude Code and Cowork is seamless (e.g., "continue this in Cowork" or vice versa)

This would transform the currently fragmented experience into a coherent platform. Right now the user has to be the glue between these products, manually re-explaining context and capabilities in each environment.

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Submitted via Claude Code by a user working with MCP integrations (bunq banking, email, calendar) and custom skills for personal finance tracking.