fix: Korean/CJK IME input and rendering in Sidebar Terminal

Fixes #1272

This commit addresses three separate Korean/CJK bugs in the Sidebar Terminal:

**Bug 1 - IME Input**: Korean text typed via IME composition was not
reaching the PTY correctly. Added compositionstart/compositionend event
listeners to suppress partial jamo fragments and only send the final
composed string.

**Bug 2a - Font Rendering**: Added CJK monospace font fallbacks
("Noto Sans Mono CJK KR", "Malgun Gothic") to both the xterm.js
fontFamily config and the CSS --font-mono variable. This ensures
consistent cell-width calculations for Korean characters.

**Bug 2b - UTF-8 Boundary Detection**: Added buffering logic to prevent
multi-byte UTF-8 characters (Korean is 3 bytes) from being split across
WebSocket chunks. This follows the same pattern as PR #1007 which fixed
the sidebar-agent path, but extends it to the terminal-agent path.

Special thanks to @ldybob for the excellent root cause analysis and
proposed solutions in issue #1272.

Tested on WSL2 + Windows 11 with Korean IME.

extension/sidepanel-terminal.js

@@ -154,7 +154,7 @@
   function ensureXterm() {
     if (term) return;
     term = new Terminal({
-      fontFamily: '"JetBrains Mono", "SF Mono", Menlo, monospace',
+      fontFamily: '"JetBrains Mono", "SF Mono", Menlo, "Noto Sans Mono CJK KR", "Malgun Gothic", monospace',
       fontSize: 13,
       theme: { background: '#0a0a0a', foreground: '#e5e5e5' },
       cursorBlink: true,
@@ -196,7 +196,25 @@
     });
     ro.observe(els.mount);
 
+    // IME composition handling for Korean/CJK input (issue #1272).
+    // Suppress partial jamo during composition; only send the final
+    // composed string on compositionend. Without this, Korean IME
+    // sends fragmented input or doubles characters.
+    let composing = false;
+    const ta = term.textarea;
+    if (ta) {
+      ta.addEventListener('compositionstart', () => { composing = true; });
+      ta.addEventListener('compositionend', (e) => {
+        composing = false;
+        if (e.data && ws && ws.readyState === WebSocket.OPEN) {
+          ws.send(new TextEncoder().encode(e.data));
+        }
+      });
+    }
+
+
     term.onData((data) => {
+      if (composing) return;  // suppress partial input events during IME composition
       if (ws && ws.readyState === WebSocket.OPEN) {
         ws.send(new TextEncoder().encode(data));
       }

extension/sidepanel.css

@@ -38,7 +38,7 @@
 
   /* Typography */
   --font-system: -apple-system, BlinkMacSystemFont, 'Segoe UI', system-ui, sans-serif;
-  --font-mono: 'JetBrains Mono', 'SF Mono', 'Fira Code', 'Cascadia Code', monospace;
+  --font-mono: 'JetBrains Mono', 'SF Mono', 'Fira Code', 'Cascadia Code', 'Noto Sans Mono CJK KR', 'Malgun Gothic', monospace;
 
   /* Radius */
   --radius-sm: 4px;