build(deps): migrate CDK app ts-node->tsx, adopt typescript 7 (INFRA-183) (#75)

ts-node 10.x is incompatible with the TypeScript 7 compiler API (cdk synth
fails with "Cannot read properties of undefined (reading 'fileExists')").
Swap the cdk.json app runner from ts-node to tsx, drop ts-node, pin tsx to
4.23.0 (matching sh-mcp), and bump typescript to ~7.0.2. Verified via
cdk synth (exit 0) and tsc build.

cdk.json

@@ -1,5 +1,5 @@
 {
-  "app": "npx ts-node --prefer-ts-exts bin/exec-aide.ts",
+  "app": "npx tsx bin/exec-aide.ts",
   "watch": {
     "include": ["**"],
     "exclude": [

package.json

@@ -13,8 +13,8 @@
   "devDependencies": {
     "@types/node": "^25.9.2",
     "aws-cdk": "^2.1125.0",
-    "ts-node": "^10.9.2",
-    "typescript": "~6.0.3"
+    "tsx": "4.23.0",
+    "typescript": "~7.0.2"
   },
   "dependencies": {
     "@aws-cdk/aws-lambda-python-alpha": "^2.180.0-alpha.0",