Add one-step Korean input setup

[MoerAI]

Korean users land on an Omarchy that can't type Hangul. The pieces are all there — fcitx5 runs in every session for the CapsLock compose sequences, and noto-fonts-cjk already renders Korean — but getting from there to typing 한글 means knowing to omarchy pkg add fcitx5-hangul, then opening fcitx5-configtool (which the launcher hides) to add the engine to the input method group. Windows and macOS finish setup with a working Korean IME; this closes that gap in one step.

What this does

• omarchy-setup-input-hangul (omarchy setup input hangul) installs fcitx5-hangul, restarts the supervised fcitx5 so it discovers the new engine, waits for it to answer, and appends hangul to the current input method group over D-Bus (org.fcitx.Fcitx.Controller1 InputMethodGroupInfo → SetInputMethodGroupInfo → Save). Existing engines stay in place, and a rerun is a no-op on the group. Without a desktop session it says so and exits 1 rather than touching anything.
• Setup > Input Method > Hangul (Korean) in the Omarchy menu runs it in the presentation terminal.
• Manual: a Typing in Korean section under Keyboard, Mouse, Trackpad — the 한/영 / Ctrl+Space toggle, the 한자 / F9 Hanja key, the korean:ralt_hangul,korean:rctrl_hanja xkb options for keyboards without dedicated keys, and the QWERTY layout Hangul needs on Dvorak or Colemak.
• Tests: test/shell.d/input-korean-test.sh pins the exact D-Bus rewrite, idempotence, the stopped-fcitx5 failure path, and that the fcitx5 state probe stays out of the terminal; menu-test.sh covers the entry; test/acceptance.d/input-korean-test.sh types Dubeolsik gks into a terminal and expects 한.

What it deliberately doesn't do

• No global fcitx5 config is written. fcitx5's stock trigger keys are Control+space, Zenkaku_Hankaku and Hangul (globalconfig.cpp), and xkb's shared symbols/pc maps the 한/영 and 한자 keys to Hangul / Hangul_Hanja on every layout, so a Korean keyboard toggles out of the box and fcitx5-hangul's defaults (Dubeolsik, Hanja on Hangul_Hanja / F9) need no hangul.conf.
• No Chromium/Electron flags. --enable-wayland-ime is no longer needed: Chromium's kWaylandTextInputV3 feature is ENABLED_BY_DEFAULT and IsImeEnabled() returns true when it is on (ui_base_features.cc, wayland_input_method_context.cc), so the Chromium Omarchy ships already talks text-input-v3 to Hyprland and on to fcitx5. The Arch wiki guidance predates that change.
• No locale, translation, install-time keyboard choice (Offer Korean as an install-time keyboard choice #9299) or bar indicator — those are separate concerns with their own PRs.

This mirrors #9634 (one-step Japanese input) on purpose: same command shape, same D-Bus group rewrite, same setup.input-method parent, so both can land and the menu reads Input Method > Hangul (Korean) / Mozc (Japanese). If #9634 goes first, the only conflict is the identical parent line. One thing found here that applies there too: a bare fcitx5-remote --check prints the input state (2) on stdout once fcitx5 answers, so the readiness probe has to be silenced or the presentation terminal shows a stray digit.

Verification

Run in an archlinux container (bind-mounted checkout, bash 5.3, jq 1.8, node 26):

Check	Result
test/shell.d/input-korean-test.sh	3 ok: fresh group gets SetInputMethodGroupInfo ssa(ss) Default us 3 keyboard-us "" keyboard-de de hangul "" + Save; hangul already present → no rewrite; fcitx5 down → exit 1, no busctl
Regression check for the probe fix	Reverting only the >/dev/null 2>&1 fails the suite with the stray 2
test/shell.d/menu-test.sh, menu-guards-test.sh	Pass
./test/cli	Pass (metadata lint, omarchy setup input hangul --help renders)
./test/shell	No new failures versus the same container before the change
Command stdout with stubbed pkg-add/busctl/fcitx5-remote	Exactly the two ready lines, exit 0, directly and via omarchy setup input hangul

Not verified: test/acceptance.d/input-korean-test.sh needs the omarchy-iso VM harness and was only syntax-checked; the full command against a live fcitx5 was exercised through stubs that answer with the real D-Bus shapes.