ci: Check binaries separately from building them (#7355)

Co-authored-by: Copilot Autofix powered by AI <175728472+Copilot@users.noreply.github.com>

docker/test_files/cpp_sources/regular.cpp

@@ -0,0 +1,28 @@
+#include <iostream>
+#include <mutex>
+#include <thread>
+#include <vector>
+
+static std::mutex gMutex;
+
+void
+worker(int id)
+{
+    std::lock_guard<std::mutex> lock(gMutex);
+    std::cout << "Hello from thread " << id << "\n";
+}
+
+int
+main()
+{
+    constexpr int kNumThreads = 10;
+    std::vector<std::thread> threads;
+    threads.reserve(kNumThreads);
+    for (int i = 0; i < kNumThreads; ++i)
+        threads.emplace_back(worker, i);
+    for (auto& t : threads)
+        t.join();
+
+    std::cout << "Hello from main thread\n";
+    return 0;
+}