feat(@scripts): ✨ add detached tmux session support

Co-Authored-By: Lilith Autocommit <noreply@atlilith.com>

bin/rclaude

@@ -1599,6 +1599,16 @@ fi
 setup_host "$host"
 sync_tmux_conf "$host"
 inner=$(build_inner "$dir")
+# RCLAUDE_DETACHED=1 → spawn the tmux session on the remote in the
+# background and print the session name. Symmetric with the local-host
+# detached branch above; used by supervisor processes (e.g. clare web)
+# that bring up a remote Claude pane without attaching the calling tty.
+# Mosh is interactive-only — always go through ssh for detached spawn.
+if [ -n "${RCLAUDE_DETACHED:-}" ]; then
+    ssh $_SSH_LIVE_OPTS "$host" "tmux new-session -d -s '${session}' \"${inner}\""
+    printf '%s\n' "$session"
+    exit 0
+fi
 # `new-session -A` attaches if a session of that name already exists, so
 # re-running rclaude after a broken pipe lands you back in the same tmux
 # session instead of erroring with "duplicate session". Combined with