Cursor/VS Code extension: teleport fails for active remote-control sessions

Description

The Claude Code extension for Cursor (and VS Code) shows remote remote-control sessions in the Web tab of the session picker. However, clicking on an active session fails with:

Error: Query closed before response received

The extension "teleports" the session (downloads history + resumes locally) instead of live-connecting to the remote-control server. This makes the Web tab unusable for its primary use case: interacting with a persistent claude remote-control session running on a remote server.

Setup

• Remote server: Ubuntu 24.04 VPS running Claude Code v2.1.97
• Session command: claude remote-control --name vps-claude-session --permission-mode acceptEdits (inside tmux)
• Local client: Cursor with Claude Code extension v2.1.96 on macOS (Apple Silicon)
• Web access: Works perfectly via claude.ai/code — can interact with the session in real-time

Reproduction

1. Start claude remote-control --name "my-session" on a remote Linux server
2. Verify the session works at claude.ai/code (it does)
3. Open Cursor → Claude Code extension → click clock icon (session history) → Web tab
4. The session appears in the list
5. Click on it → "Error: Query closed before response received"

What happens (from output logs)

Teleport started for session session_01JDmke1vP4tH7MwvDmRMUUY
Fetched 0 log entries for session session_01JDmke1vP4tH7MwvDmRMUUY
Saved teleported session 797c2b62-d1e9-4407-a5cf-f9c1c5ac6a5b with 0 messages
Teleport succeeded for session session_01JDmke1vP4tH7MwvDmRMUUY in 409ms (0 messages)

Then the extension tries to resume locally:

Spawning Claude with SDK query function - cwd: /Users/gustavo_saborio, resume: 797c2b62-d1e9-4407-a5cf-f9c1c5ac6a5b

The local Claude process starts, initializes, then immediately shuts down:

LSP server manager shut down successfully
Error spawning Claude (on channel nftorcyc7up): Error: Query closed before response received

Root causes

1. Teleport fetches 0 messages from an active session — it can't clone a live session
2. Tries to resume locally on macOS instead of connecting to the remote server — wrong cwd (/Users/... vs /root), wrong OS, no access to remote filesystem
3. No live-connect capability — the extension only supports download-and-replay, not bridging to a running remote-control server

Expected behavior

Clicking a remote-control session in the Web tab should live-connect to the remote session (similar to how claude.ai/code does it), not teleport/download it. The remote-control protocol already supports this — the web app proves it works.

Alternatively, if live-connect isn't feasible in the extension, the Web tab should either:

• Clearly indicate that active sessions can't be teleported
• Open claude.ai/code in the browser for that session

Environment

• Extension version: 2.1.96 (Cursor, darwin-arm64)
• Remote CLI version: 2.1.97
• OS: macOS (client) / Ubuntu 24.04 (server)