/branch (/fork) always fails with 'No conversation to branch' in background (daemon-backed thin-client) sessions

Bug

/branch (and its alias /fork) always fails with Failed to branch conversation: No conversation to branch when invoked against a background session (daemon-backed thin-client REPL — e.g., the bg/Agents view).

The session JSONL exists on disk under the expected project directory, so the conversation data is there — it just isn't reachable from /branch in thin-client mode.

Environment

• Claude Code 2.1.143
• macOS 26.4.1 (arm64)

Repro

1. Start a background session (Agents View / bg job).
2. In the thin-client view of that session, type /branch (or /fork).
3. → Failed to branch conversation: No conversation to branch

(Same /branch works fine from a normal local REPL session in the same project.)

Evidence the conversation is on disk

State of the bg session I tested:

~/.claude/jobs/<short>/state.json:
  "sessionId": "923d0a88-3740-4f2c-beb8-76dc32051900",
  "resumeSessionId": "923d0a88-3740-4f2c-beb8-76dc32051900",
  "bridgeSessionId": "cse_01UWkiSRXQbWGRsn8o9wJefR",
  "backend": "daemon",
  "cwd": "/Users/me/projects/foo",
  "originCwd": "/Users/me/projects/foo",

The corresponding jsonl is on disk and accumulating messages normally:

~/.claude/projects/-Users-me-projects-foo/923d0a88-3740-4f2c-beb8-76dc32051900.jsonl  (25 lines, growing)

So this is not a missing-conversation issue — /branch is failing despite a perfectly valid session file at the expected location.

Observed behavior

• The failure is 100% reproducible in any bg/thin-client session, regardless of message count, regardless of project (tested across multiple repos).
• The same command in a normal foreground REPL on the same project succeeds.
• The cwd of the bg session matches its originCwd, so this is not the EnterWorktree-induced cwd-change case from #48254.
• /btw <question> followed by the f (fork) hotkey does work from the same bg session — suggesting the fork machinery itself isn't broken, only /branch's entry point isn't routed correctly for thin-client mode.

Related (not duplicates)

• #48254 — same error string, but root cause is cwd-change via EnterWorktree resolving the project dir to a different folder. Different mechanism; my session's cwd is stable and matches originCwd, and the error reproduces without ever entering a worktree.
• #45179 / #48110 — submodule/bare-repo worktree path-resolution issues for /resume, not /branch in thin-client mode.

Suggested fix

Route /branch through the daemon when invoked from a thin-client REPL, the same way /btw's fork hotkey works in bg sessions today. Whatever predicate distinguishes thin-client/bg from local REPL for /btw should gate /branch's dispatch as well.