fix: implement random-port discovery for CI E2E backend

When PORT=0, the backend now writes its actual bound port to
data/test/.port. test-env.sh reads that file when TT_TEST_PORT=0
so all targets (test-up, test-reset, test-down) resolve the real URL.
test-up waits for .port to appear before the health-check loop.

Makefile

@@ -60,10 +60,19 @@ test-up:
 		exit 0; \
 	fi; \
 	[ -f "$$TT_TEST_DB" ] || $(MAKE) test-rebuild; \
+	rm -f data/test/.port; \
 	DATABASE_URL="sqlite:$$TT_TEST_DB" PORT=$$TT_TEST_PORT TT_TEST_MODE=1 JWT_SECRET=testsecret STATIC_DIR=frontend/build \
 		cargo run --manifest-path backend/Cargo.toml &>/tmp/tutortool-test.log & \
 	echo $$! > data/test/.pid; \
 	echo "[test-up] Backend PID $$(cat data/test/.pid) starting on port $$TT_TEST_PORT..."; \
+	if [ "$$TT_TEST_PORT" = "0" ]; then \
+		for i in $$(seq 1 30); do \
+			[ -f data/test/.port ] && break; \
+			sleep 1; \
+		done; \
+		. scripts/test-env.sh; \
+		echo "[test-up] Backend bound to port $$TT_TEST_PORT"; \
+	fi; \
 	for i in $$(seq 1 30); do \
 		curl -fs "$$TT_BASE_URL/health" >/dev/null 2>&1 && break; \
 		sleep 1; \

backend/src/main.rs

@@ -85,7 +85,14 @@ async fn main() {
     let listener = tokio::net::TcpListener::bind(&addr)
         .await
         .expect("failed to bind");
-    tracing::info!("listening on {}", addr);
+    let actual_addr = listener.local_addr().expect("failed to get local addr");
+    tracing::info!("listening on {}", actual_addr);
+
+    // When started with PORT=0 (random), write actual port so the test harness can discover it
+    if port == "0" {
+        let _ = std::fs::create_dir_all("data/test");
+        let _ = std::fs::write("data/test/.port", actual_addr.port().to_string());
+    }
 
     axum::serve(
         listener,

scripts/test-env.sh

@@ -13,6 +13,15 @@ if [ "${TT_TEST_PORT_RANDOM:-0}" = "1" ]; then
   TT_TEST_PORT=0
 fi
 
+# If port is 0 and the backend already wrote its actual port, use it
+_port_file="${TT_WORKTREE_ROOT}/data/test/.port"
+if [ "$TT_TEST_PORT" = "0" ] && [ -f "$_port_file" ]; then
+  _real_port=$(cat "$_port_file")
+  if [ -n "$_real_port" ] && [ "$_real_port" != "0" ]; then
+    TT_TEST_PORT=$_real_port
+  fi
+fi
+
 TT_TEST_DB="${TT_WORKTREE_ROOT}/data/test/attendance.db"
 TT_TEST_MODE=1
 TT_BASE_URL="http://127.0.0.1:${TT_TEST_PORT}"