Claude Max: No MCP support in web UI & no way to continue web UI conversations in Claude Code

Problem

Paying Claude Max customer unable to use MCP integrations (specifically Etherscan MCP) with long-running research conversations in the claude.ai web UI.

Core issues:

1. claude.ai web UI does not support MCP servers — customers paying for Max cannot connect MCP tools (Etherscan, GitHub, etc.) to their web conversations
2. No way to transfer/continue a claude.ai conversation in Claude Code — long-running research with significant built-up context is trapped in the web UI with no path to move it to Claude Code where MCP is supported
3. Product gap creates a broken workflow — the two interfaces (web UI and Claude Code) are completely siloed, forcing customers to choose between conversation continuity and MCP tool access

Impact

This makes Claude Max feel non-functional for users who need both long-running research conversations AND MCP tool access. Customers are paying premium prices for capabilities that don't work together.

Requested solution

• Add MCP support to claude.ai web UI, OR
• Provide a way to export/continue web UI conversations in Claude Code with full context preserved

Filed on behalf of a frustrated Claude Max customer.