fix: copy serve.ts into the Docker build stage

The image build ran the tests without serve.ts present, so the server the
tests spawn never started and the hook stalled until it timed out. The
runtime stage would have failed on the same missing file immediately after.

The test now bails the moment the process exits and reports its stderr, so
this shows up as "serve.ts exited with 1 before listening" in 53ms rather
than an unexplained hook timeout after five seconds.

serve.ts is also in tsconfig's include now — it was outside it, so a type
error in the file that serves the app would only have surfaced at runtime.
Adding it immediately caught one in the test.

Verified by replaying the build stage against exactly the copied file set.

Co-Authored-By: Claude Opus 5 (1M context) <[email protected]>

tsconfig.json

@@ -16,5 +16,5 @@
     "jsx": "react-jsx",
     "verbatimModuleSyntax": true
   },
-  "include": ["src", "test", "scripts"]
+  "include": ["src", "test", "scripts", "serve.ts"]
 }