feat: add build info API endpoint

Add API route to serve deployment information and TypeScript definitions for type safety.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/app/api/build-info/route.ts

@@ -0,0 +1,6 @@
+import { NextResponse } from 'next/server'
+import buildInfo from '@/generated/build-info.json'
+
+export async function GET() {
+  return NextResponse.json(buildInfo)
+}

apps/web/src/types/build-info.d.ts

@@ -0,0 +1,20 @@
+declare module '@/generated/build-info.json' {
+  interface BuildInfo {
+    version: string
+    buildTime: string
+    buildTimestamp: number
+    git: {
+      commit: string | null
+      commitShort: string | null
+      branch: string | null
+      tag: string | null
+      isDirty: boolean
+    }
+    environment: string
+    buildNumber: string | null
+    nodeVersion: string
+  }
+
+  const buildInfo: BuildInfo
+  export default buildInfo
+}