[Feature Request] Unified agent identity and context across clients (CLI, Desktop App, Mobile)

Problem Statement

Today, Claude Code (CLI), the Claude Desktop App, and the Claude Mobile App each start independent conversations with no shared context. A user working on the same project across multiple clients — CLI for deep development, Desktop App for conversation and planning, Mobile for quick dispatch — must re-explain context to each client separately. Each client instantiates a separate Claude with no awareness of what the others have done.

This forces power users to build manual workarounds: shared state files on disk, memory systems that each client reads at boot, and hand-rolled session handoff protocols. These work, but they're fragile and shouldn't be the user's responsibility.

Proposed Solution

Introduce a unified agent identity scoped to a project (or workspace). When multiple clients connect to the same project:

1. Shared conversation context — All clients contribute to and read from a single thread of agent state. A decision made via Mobile is known to the CLI session without re-stating it.

1. Client-appropriate interaction modes — The same agent identity adapts its interface to the client:

• CLI: code-focused, tool-heavy
• Desktop App: conversational, visual previews
• Mobile: concise, voice-ready (when available)

1. Persistent memory across sessions — The agent remembers prior sessions' decisions, corrections, and project state without the user maintaining external memory files. This is distinct from (and complementary to) project-level CLAUDE.md instructions.

1. Session handoff — Explicit or implicit handoff between clients. "Continue this in VS Code" should carry full context, not just a branch name.

Use Case

A developer working on a long-running project (months/years) uses:

• Claude Code in VS Code for implementation, testing, and CI work
• Claude Desktop App for architecture discussions, planning, and reviewing agent work
• Claude Mobile for quick status checks, approvals, and dispatch while away from desk

All three clients are open against the same repository. The developer expects the same agent awareness regardless of which client they speak through — similar to how a human collaborator doesn't lose memory when you switch from Slack to a face-to-face conversation.

Current Workaround

Users can partially solve this today by:

• Writing shared state to files in the repo (e.g., HEARTBEAT.md, next_task.md) that each client reads via CLAUDE.md boot instructions
• Using skills/slash commands (/boot, /tick) to reload state at session start
• Relying on git as the synchronization layer

This works but requires significant setup, is invisible to most users, and puts architectural burden on the user rather than the platform.

Why This Matters

Claude is converging on multi-client usage. The authorization token system already shows multiple Claude Code connections per project. The Desktop App already supports session handoff to VS Code. Mobile already supports the same account. The infrastructure is partially there — what's missing is the identity layer that ties them together.

Users who invest in Claude as a long-term collaborator (not a one-shot Q&A tool) need continuity. The model provides capability; identity provides continuity. Both are required for durable human-agent collaboration.

Success Criteria

• A user can ask "what did we decide about X?" from any client and get a correct answer, even if that decision was made in a different client
• Agent state (corrections, preferences, project knowledge) persists across client switches without user intervention
• No manual boot/sync protocol required