refactor(editor): migrate to Milkdown with LaTeX support and clean up legacy code

- Removed old contenteditable-based MarkdownEditor component
- Integrated Milkdown Crepe with LaTeX (KaTeX) rendering support
- Simplified inline suggestion plugin using ProseMirror decorations
- Removed debug logging and unused components (HelloWorld, plan files)
- Increased debounce from 150ms to 500ms for better performance
- Fixed SSE JSON serialization in backend main.py

package-lock.json

@@ -2008,13 +2008,13 @@
       "license": "MIT"
     },
     "node_modules/axios": {
-      "version": "1.13.2",
-      "resolved": "https://registry.npmjs.org/axios/-/axios-1.13.2.tgz",
-      "integrity": "sha512-VPk9ebNqPcy5lRGuSlKx752IlDatOjT9paPlm8A7yOuW2Fbvp4X3JznJtT4f0GzGLLiWE9W8onz51SqLYwzGaA==",
+      "version": "1.13.5",
+      "resolved": "https://registry.npmjs.org/axios/-/axios-1.13.5.tgz",
+      "integrity": "sha512-cz4ur7Vb0xS4/KUN0tPWe44eqxrIu31me+fbang3ijiNscE129POzipJJA6zniq2C/Z6sJCjMimjS8Lc/GAs8Q==",
       "license": "MIT",
       "dependencies": {
-        "follow-redirects": "^1.15.6",
-        "form-data": "^4.0.4",
+        "follow-redirects": "^1.15.11",
+        "form-data": "^4.0.5",
         "proxy-from-env": "^1.1.0"
       }
     },
@@ -2513,9 +2513,10 @@
       }
     },
     "node_modules/lodash-es": {
-      "version": "4.17.22",
-      "resolved": "https://registry.npmjs.org/lodash-es/-/lodash-es-4.17.22.tgz",
-      "integrity": "sha512-XEawp1t0gxSi9x01glktRZ5HDy0HXqrM0x5pXQM98EaI0NxO6jVM7omDOxsuEo5UIASAnm2bRp1Jt/e0a2XU8Q=="
+      "version": "4.17.23",
+      "resolved": "https://registry.npmjs.org/lodash-es/-/lodash-es-4.17.23.tgz",
+      "integrity": "sha512-kVI48u3PZr38HdYz98UmfPnXl2DXrpdctLrFLCd3kOx1xUkOmpFPx7gCWWM5MPkL/fD8zb+Ph0QzjGFs4+hHWg==",
+      "license": "MIT"
     },
     "node_modules/longest-streak": {
       "version": "3.1.0",