[FEATURE] In Desktop SSH sessions, allow WebFetch to run on the local host instead of the remote SSH target

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When using Claude Code Desktop over SSH, I want WebFetch to run on the local desktop host, while shell/file/code operations continue to run on the remote machine.

In remote compute environments, outbound network access is often restricted or routed differently. That is fine for code execution, but it makes doc/web retrieval unnecessarily hard. Since Claude Code Desktop itself is running locally, it would be very useful to let WebFetch use the local machine's network path.

Proposed Solution

Please add an option for Desktop SSH sessions to route WebFetch through the local host only.

• Remote: Bash, file edits, git, tests
• Local: WebFetch

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

_No response_

Additional Context

This seems related, but distinct from:

#53511 (WebFetch permissions vs sandbox network allowlist coupling)
#31296 and #38735 (current coupling between WebFetch rules and sandbox network behavior)

This request is specifically about Desktop SSH sessions and allowing WebFetch to execute on the local host instead of the remote SSH target.