feat: register sessions with claude-sessions on spawn

After tmux new-session, call claude-sessions register with the
project_dir, profile, mode, and session name. Non-fatal — if
claude-sessions is not installed the spawn still proceeds.

scripts/claude-tmux

@@ -141,6 +141,16 @@ tmux new-session -d -s "$NAME" -c "$PROJECT_DIR"
 tmux send-keys -t "$NAME" -l "$LAUNCH_CMD"
 tmux send-keys -t "$NAME" Enter
 
+# Register with claude-sessions registry (non-fatal)
+if command -v claude-sessions &>/dev/null; then
+    claude-sessions register \
+        --project-dir "$PROJECT_DIR" \
+        --profile "$PROFILE" \
+        --mode "$MODE" \
+        --tmux-name "$NAME" \
+        2>/dev/null || true
+fi
+
 echo -e "${GREEN}Spawned${NC} tmux session: $NAME"
 echo "  dir:     $PROJECT_DIR"
 echo "  profile: $PROFILE / mode: $MODE"