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.

install/provisioning/setup-form.sh

@@ -17,7 +17,10 @@
 # only keys any gum widget exits on, and Ctrl+C arrives as a byte in raw mode,
 # so it never reaches the shell as SIGINT. Act on the status, never on a trap.
 #
-# Callers supply `notice <message> <seconds>` and set every variable these prompts write.
+# Callers supply `notice <message> <seconds>` for validation feedback, and set
+# the variables these prompts write: keyboard, keyboard_label,
+# keyboard_input_method, keyboard_xkb_layout, username,
+# password, password_confirmation, full_name, email_address, hostname, timezone.
 
 OMARCHY_FORM_BACK=1
 OMARCHY_FORM_SIGNAL=130
@@ -35,6 +38,8 @@ Azerbaijani|azerty
 Belarusian|by
 Belgian|be-latin1
 Bulgarian|bg-cp1251
+Chinese (Simplified, Pinyin)|us|pinyin
+Chinese (Traditional, Zhuyin)|us|chewing
 Croatian|croat
 Czech|cz
 Danish|dk-latin1
@@ -53,8 +58,10 @@ Hungarian|hu
 Icelandic|is-latin1
 Irish|ie
 Italian|it
-Japanese|jp106
+Japanese|jp106|mozc
+Japanese (US keyboard)|us|mozc
 Kazakh|kazakh
+Korean|us|hangul|kr
 Kyrgyz|kyrgyz
 Lao|la-latin1
 Latvian|lv
@@ -146,8 +153,22 @@ omarchy_prompt_keyboard() {
     gum choose --height 10 --selected "English (US)" --header "$(omarchy_text "Select keyboard layout")") && status=0 || status=$?
   ((status == 0)) || return $status
 
-  keyboard_label="$choice"
-  keyboard=$(printf '%s\n' "$OMARCHY_KEYBOARD_LAYOUTS" | awk -F'|' -v c="$choice" '$1==c{print $2; exit}')
+  local selection
+  selection=$(printf '%s\n' "$OMARCHY_KEYBOARD_LAYOUTS" | awk -F'|' -v c="$choice" '$1==c{print; exit}')
+  [[ -n $selection ]] || return 1
+  IFS='|' read -r keyboard_label keyboard keyboard_input_method keyboard_xkb_layout <<< "$selection"
+  keyboard_input_method=${keyboard_input_method:-none}
+  keyboard_xkb_layout=${keyboard_xkb_layout:-}
+}
+
+# Root-side persistence. Console keymaps remain real keymaps; the input
+# preference survives separately for every user of the installed system.
+omarchy_persist_input_selection() {
+  local target_root=${1:-} method=${keyboard_input_method:-none} layout=${keyboard_xkb_layout:-}
+  case "$method" in none | mozc | hangul | pinyin | chewing) ;; *) return 1 ;; esac
+  case "$layout" in "" | kr) ;; *) return 1 ;; esac
+  mkdir -p "$target_root/etc/omarchy"
+  printf 'INPUT_METHOD=%s\nXKB_LAYOUT=%s\n' "$method" "$layout" > "$target_root/etc/omarchy/input-method"
 }
 
 omarchy_prompt_username() {