Merge #14433 input methods and remove Rime

The keyboard choice and omarchy-setup-input own Chinese input now. The
new passwordless sudo and input tooltips get Chinese text.

bin/omarchy-region

@@ -33,7 +33,7 @@ if [[ $channel != "stable" && $channel != "rc" && $channel != "edge" ]]; then
 fi
 
 if [[ $1 == "cn" ]]; then
-  # Packages first against current mirrors, so a failed install leaves the machine Global.
+  # Upgrade first: the keyring install below syncs new databases.
   omarchy-update-pacman -Syu --noconfirm
   sudo env OMARCHY_REGION=cn OMARCHY_PATH="$OMARCHY_PATH" bash -e "$OMARCHY_PATH/install/config/region.sh"
   # Trust ArchLinuxCN before the refresh upgrades through it.
@@ -44,11 +44,6 @@ if [[ $1 == "cn" ]]; then
   sudo pacman --config "$rendered/pacman.conf" -Sy --noconfirm --needed "${profile_packages[@]}"
   sudo pacman-key --populate archlinuxcn
   omarchy-refresh-pacman "$channel"
-  if [[ ! -f $HOME/.local/share/fcitx5/rime/rime_ice.schema.yaml ]]; then
-    # A running fcitx5 only sees the new Rime addon after a restart.
-    systemctl --user try-restart omarchy-fcitx5.service
-    rime-ice-installer --yes
-  fi
 else
   sudo env OMARCHY_REGION=global OMARCHY_PATH="$OMARCHY_PATH" bash -e "$OMARCHY_PATH/install/config/region.sh"
   omarchy-refresh-pacman "$channel"