Add missing standard library header inclusions (#5316)

Discovered by clang-tidy.

testing/file_test/autoupdate.cpp

@@ -5,6 +5,8 @@
 #include "testing/file_test/autoupdate.h"
 
 #include <fstream>
+#include <string>
+#include <utility>
 
 #include "absl/strings/str_replace.h"
 #include "absl/strings/string_view.h"

testing/file_test/file_test_base.cpp

@@ -21,9 +21,16 @@
 
 #include "testing/file_test/file_test_base.h"
 
+#include <atomic>
+#include <cstdlib>
 #include <filesystem>
+#include <functional>
+#include <memory>
+#include <mutex>
 #include <optional>
 #include <string>
+#include <string_view>
+#include <system_error>
 #include <utility>
 
 #include "absl/flags/flag.h"

testing/file_test/file_test_base_test.cpp

@@ -7,6 +7,11 @@
 #include <gmock/gmock.h>
 #include <gtest/gtest.h>
 
+#include <functional>
+#include <memory>
+#include <optional>
+#include <string>
+
 #include "common/ostream.h"
 #include "llvm/ADT/StringExtras.h"
 #include "llvm/ADT/StringSwitch.h"

testing/file_test/manifest.cpp

@@ -4,6 +4,8 @@
 
 #include "testing/file_test/manifest.h"
 
+#include <string>
+
 // The test manifest, produced by `manifest_as_cpp`.
 // NOLINTNEXTLINE(readability-identifier-naming): Constant in practice.
 extern const char* CarbonFileTestManifest[];

testing/file_test/run_test.cpp

@@ -6,6 +6,9 @@
 
 #include <gtest/gtest.h>
 
+#include <string>
+#include <utility>
+
 #include "llvm/ADT/ScopeExit.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/StringMap.h"

testing/file_test/test_file.cpp

@@ -5,6 +5,9 @@
 #include "testing/file_test/test_file.h"
 
 #include <fstream>
+#include <optional>
+#include <string>
+#include <utility>
 
 #include "common/check.h"
 #include "common/error.h"