refactor: floating and topic ai

package.json

@@ -32,6 +32,7 @@
     "test:e2e": "playwright test"
   },
   "dependencies": {
+    "@ai-sdk/react": "2.0.0-beta.34",
     "@astrojs/node": "^9.2.1",
     "@astrojs/react": "^4.2.7",
     "@astrojs/sitemap": "^3.4.0",
@@ -43,6 +44,7 @@
     "@radix-ui/react-popover": "^1.1.14",
     "@resvg/resvg-js": "^2.6.2",
     "@roadmapsh/editor": "workspace:*",
+    "@shikijs/transformers": "^3.9.2",
     "@tailwindcss/vite": "^4.1.7",
     "@tanstack/react-query": "^5.76.1",
     "@tiptap/core": "^2.12.0",
@@ -65,6 +67,7 @@
     "image-size": "^2.0.2",
     "jose": "^6.0.11",
     "js-cookie": "^3.0.5",
+    "katex": "^0.16.22",
     "lucide-react": "^0.511.0",
     "luxon": "^3.6.1",
     "markdown-it-async": "^2.2.0",
@@ -80,10 +83,14 @@
     "react-confetti": "^6.4.0",
     "react-dom": "^19.1.0",
     "react-dropzone": "^14.3.8",
+    "react-markdown": "^10.1.0",
     "react-resizable-panels": "^3.0.2",
     "react-textarea-autosize": "^8.5.9",
     "react-tooltip": "^5.28.1",
     "rehype-external-links": "^3.0.0",
+    "rehype-katex": "^7.0.1",
+    "remark-gfm": "^4.0.1",
+    "remark-math": "^6.0.0",
     "remark-parse": "^11.0.0",
     "roadmap-renderer": "^1.0.7",
     "sanitize-html": "^2.17.0",
@@ -98,6 +105,7 @@
     "tiptap-markdown": "^0.8.10",
     "turndown": "^7.2.0",
     "unified": "^11.0.5",
+    "zod": "^4.0.17",
     "zustand": "^5.0.4"
   },
   "devDependencies": {
@@ -113,7 +121,7 @@
     "@types/react-slick": "^0.23.13",
     "@types/sanitize-html": "^2.16.0",
     "@types/turndown": "^5.0.5",
-    "ai": "^4.3.16",
+    "ai": "5.0.0-beta.34",
     "csv-parser": "^3.2.0",
     "gh-pages": "^6.3.0",
     "js-yaml": "^4.1.0",