Detect the missing official repo dbs by core.db, not any db

pacstrap leaves the offline repo's db in the target's sync dir, so
the any-db glob skipped the first-run update path on real installs.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QKxGW1raAWaqeU8WdHsMsp

bin/omarchy-cn-app-install

@@ -32,9 +32,10 @@ fi
 
 case "$source_type" in
 aur)
-  # Offline installs ship no sync db; yay then treats repo deps as AUR.
-  # System upgrades must go through the omarchy-update pipeline (pacman guard).
-  if ! compgen -G "/var/lib/pacman/sync/*.db" > /dev/null; then
+  # Offline installs leave only offline.db in sync; without the official
+  # repo dbs yay treats repo deps as AUR. Upgrades must go through the
+  # omarchy-update pipeline (pacman guard).
+  if [[ ! -f /var/lib/pacman/sync/core.db ]]; then
     if [[ ! -t 0 ]]; then
       echo "首次安装应用前请先完成一次系统更新: omarchy-update" >&2
       exit 1