Bridge child processes get a machine-settings mode

What

• When Claude Code spawns a Remote Control bridge worker child process, it can now set a new environment variable, CLAUDE_CODE_BRIDGE_CHILD_MACHINE_SETTINGS="1", alongside the existing CLAUDE_CODE_BRIDGE_CHILD_AUTO_DEFAULT and CLAUDE_CODE_BRIDGE_CHILD_ARTIFACT variables. This is set for project-thread child sessions when a related feature flag is on.
• When this bridge-child machine-settings mode is active, Claude-in-Chrome (the browser integration, referred to as CFC) is no longer turned on by default in cases where it otherwise would be.

Why

This lets bridge child sessions run with their own machine-level settings without unexpectedly also turning on the Chrome browser integration by default.