fix(cjk): hide CJK textarea on welcome screen and fix vertical centering

- Guard `_updateCjkInputState()` with `activeSessionId` check so the
  `position: fixed` CJK textarea doesn't float over the welcome overlay
- Call `_updateCjkInputState()` in `showWelcome()`/`hideWelcome()` to
  sync CJK visibility on session enter/leave
- Add `padding: 12px 10px` to `.cjk-input-visible textarea` for proper
  vertical centering of input text

src/web/public/terminal-ui.js

@@ -943,6 +943,9 @@ Object.assign(CodemanApp.prototype, {
       this.loadTunnelStatus();
       this.loadHistorySessions();
     }
+    // Home screen has no input target — hide the CJK textarea (activeSessionId
+    // is null by the time we get here). Guarded: defined on the app object.
+    this._updateCjkInputState?.();
   },
 
   hideWelcome() {
@@ -956,6 +959,9 @@ Object.assign(CodemanApp.prototype, {
       clearTimeout(this._welcomeQrShrinkTimer);
       qrWrap.classList.remove('expanded');
     }
+    // Entering a session — restore CJK textarea if the user has it enabled
+    // (activeSessionId is already set by selectSession before this call).
+    this._updateCjkInputState?.();
   },
 
   /**