[FEATURE] Support local persistence of .claude/CLAUDE.md when working on remote SSH servers

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 working on ephemeral remote servers via SSH (common in cloud development environments, CI/CD systems, or containerized workflows), the .claude/ directory and CLAUDE.md memory file must be recreated on each new server instance. This creates friction as users lose their accumulated context and instructions every time they spin up a new environment.

Currently, Claude Code requires .claude/CLAUDE.md to exist on the remote filesystem where it's running. For ephemeral infrastructure, this means:

• Users must manually recreate their memory files on each new server
• Context and instructions are lost between sessions
• No straightforward way to maintain persistent configuration across temporary environments

Proposed Solution

Add configuration options to specify a local fallback location for .claude/CLAUDE.md when working on remote servers:

1. Option 1: Local Mirror Directory

• Allow users to configure a local path in settings (e.g., ~/.claude/remote-mirrors/)
• Claude Code automatically syncs CLAUDE.md from local to remote on connection
• Changes made remotely can optionally sync back to local

1. Option 2: Settings-based Fallback

• Add claudeMemory.localPath setting in user settings
• Claude Code reads from local path when remote .claude/CLAUDE.md doesn't exist
• Example: "claudeMemory.localPath": "~/.claude/CLAUDE.md"

1. Option 3: Auto-sync on SSH Connection

• Detect SSH remote connections
• Automatically copy local .claude/CLAUDE.md to remote project on initialization
• Offer to sync changes back on disconnect

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Configuration and settings

Use Case Example

Developer workflow:

1. Works on ephemeral AWS Cloud9 / Gitpod / GitHub Codespaces environment
2. Accumulates important context in .claude/CLAUDE.md over several days
3. Environment times out or is deleted (ephemeral by design)
4. Spins up new environment for next session
5. Currently: Must recreate CLAUDE.md manually or commit to git
6. Desired: Claude Code automatically syncs from ~/.claude/CLAUDE.md on local machine

Additional Context

• This is particularly relevant for:
• Cloud-based development environments (AWS Cloud9, Gitpod, GitHub Codespaces)
• Container-based development with ephemeral volumes
• CI/CD environments where Claude Code might assist with debugging
• Development teams using rotating infrastructure for security/cost reasons
• Committing CLAUDE.md to git isn't always ideal because:
• Memory files often contain developer-specific preferences
• May include sensitive project context that shouldn't be shared
• Creates unnecessary git noise with frequent updates
• Similar functionality exists in other tools (e.g., VS Code Remote SSH extension syncing certain settings

from local to remote)