build(deps): migrate CDK app ts-node->tsx, adopt typescript 7 (INFRA-183) (#39)

ts-node 10.x is incompatible with the TypeScript 7 compiler API (cdk synth
fails with "Cannot read properties of undefined (reading 'fileExists')").
Switch the cdk.json app runner to tsx (pinned 4.23.0, matching sh-mcp) and
bump typescript to ~7.0.2. Synthesized templates are byte-identical across
all six stacks; toolchain-only change.

cdk.json

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

package.json

@@ -16,8 +16,8 @@
     "@types/source-map-support": "^0.5.10",
     "aws-cdk": "^2.1129.0",
     "source-map-support": "^0.5.21",
-    "ts-node": "^10.9.2",
-    "typescript": "~6.0.3"
+    "tsx": "4.23.0",
+    "typescript": "~7.0.2"
   },
   "dependencies": {
     "aws-cdk-lib": "2.261.0",