[FEATURE] Make the mobile Code tab a native client for agent-view background sessions

Preflight

• [x] I searched existing requests — no issue covers this. The nearest, #57543, asks for SSH/Mosh to the mobile app (a better terminal); this asks for the opposite — a native client with no terminal involved.
• [x] This is a single feature request.

Problem Statement

claude agents (agent view) is the best multi-session experience in Claude Code: a multiplexed view of persistent background conversations, supervisor-managed, grouped by Working / Needs input / Ready for review, surviving sleep and reattachable after restart. It is excellent — at the desk.

It is also local-only, and the mobile story doesn't follow from it:

1. The only way to reach these background agents from a phone today is to SSH into the host and use the agent-view TUI in a mobile terminal (e.g. Termius). A full-screen TUI over SSH on a phone is genuinely painful — tiny targets, key-chord shortcuts, no native scroll or notifications.
2. claude remote-control is native on mobile but operates a completely separate session pool. Sessions I started in agent view never appear there; it has no introspection into the supervisor's background agents. Two disconnected universes.

Net: I have a fleet of persistent agents running great on an always-on machine, and no native, terminal-free way to check or steer them from my phone — which is exactly when I'm away from the desk and a session goes "Needs input."

Proposed Solution

Make the native mobile Code tab a client for the agent-view session pool — render the same supervisor-managed background sessions natively, no SSH terminal in the loop.

Concretely, the mobile Code tab would:

• List the background sessions agent view shows, with live status (Working / Needs input / Ready for review / Completed) and the one-line summaries agent view already generates.
• Open a session into its full conversation; send a message / answer a "needs input" prompt; return to the list — the core agent-view loop, rendered natively.
• Treat each session as one shared object across desktop TUI, desktop Code tab, and mobile — a client view, not a copy. Lifecycle stays owned by the supervisor/daemon on the host; mobile never spawns a parallel pool.

Surface could be a flag on the existing server (claude remote-control --attach-agents) or a "serve to mobile" toggle in agent view — design detail, not the ask. The ask is: the agents I already run show up natively on my phone.

Alternative Solutions

• SSH/Mosh to the TUI (#57543) — the workaround I use today and explicitly want to eliminate; it improves the terminal path rather than removing it.
• claude remote-control — native, but a separate pool with no view of the background agents; no multiplexed manager, no reboot-reattach model.
• Cloud Code-tab sessions — native and synced, but ephemeral cloud VMs with none of my local environment; not the persistent local agents I'm already running.
• Telegram/Discord channels — event-driven nudging, not a native session UI.

Use Case Example

1. I have 6 background agents running under claude agents on my always-on desktop; I leave for lunch.
2. On my phone, in the native Claude app's Code tab (no SSH, no terminal), I see all 6 with live status. One is Needs input.
3. I open it, answer the question, watch it continue.
4. Back at my desk, that same session is still right there in the agent-view TUI, mid-stream — same object, not a copy.

Additional Context

• Should be a client/transport addition, not a new session model — the supervisor already owns lifecycle and persistence; this exposes that pool to an existing native surface. No change to how sessions run or persist.
• Related: #57543 (SSH/Mosh to mobile — opposite mechanism), #48965 (multi-session coordination primitives — plausible shared infrastructure), #61160 (richer Remote Control mobile UI — same surface, RC's own pool).
• Future extension (out of scope for this request): a push notification when a background session transitions to "Needs input" would make the mobile client genuinely set-and-forget — but listing + attach + respond is the core ask.

---

Priority: Medium
Feature Category: Other — Remote Control / mobile (agent view)