[mcp] Fix package.json (#33101)

Since we use esbuild we need to correctly move dependencies that are
required at runtime into `dependencies` and other packages that are only
used in development in to `devDependencies`. This ensures the correct
packages are included in the build.
---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/facebook/react/pull/33101).
* #33085
* #33084
* #33083
* #33082
* __->__ #33101

Author: poteto

compiler/packages/react-mcp-server/package.json

@@ -15,25 +15,22 @@
   "dependencies": {
     "@babel/core": "^7.26.0",
     "@babel/parser": "^7.26",
-    "@babel/plugin-syntax-typescript": "^7.25.9",
+    "@babel/preset-env": "^7.26.9",
+    "@babel/preset-react": "^7.18.6",
+    "@babel/preset-typescript": "^7.27.1",
     "@modelcontextprotocol/sdk": "^1.9.0",
-    "@types/jest": "^29.5.14",
     "algoliasearch": "^5.23.3",
     "cheerio": "^1.0.0",
     "html-to-text": "^9.0.5",
-    "jest": "^29.7.0",
     "prettier": "^3.3.3",
     "puppeteer": "^24.7.2",
-    "ts-jest": "^29.3.2",
     "zod": "^3.23.8"
   },
   "devDependencies": {
-    "@babel/plugin-proposal-class-properties": "^7.18.6",
-    "@babel/plugin-transform-runtime": "^7.26.10",
-    "@babel/preset-env": "^7.26.9",
-    "@babel/preset-react": "^7.26.3",
-    "@babel/preset-typescript": "^7.27.0",
-    "@types/html-to-text": "^9.0.4"
+    "@types/html-to-text": "^9.0.4",
+    "@types/jest": "^29.5.14",
+    "jest": "^29.7.0",
+    "ts-jest": "^29.3.2"
   },
   "license": "MIT",
   "repository": {