Run pub get before building host.dart. (#37502)

* Run pub get before building host.dart.

* We should call `pub get` for `web_ui` in the launcher script because
felt itself needs it. However, we should let felt invoke `pub get` on
`web_engine_tester` only as needed, not in the launcher script.

lib/web_ui/dev/felt

@@ -87,11 +87,9 @@ then
 fi
 
 install_deps() {
+  # We need to run pub get here before we actually invoke felt.
   echo "Running \`dart pub get\` in 'engine/src/flutter/lib/web_ui'"
   (cd "$WEB_UI_DIR"; $DART_PATH pub get)
-
-  echo "Running \`dart pub get\` in 'engine/src/flutter/web_sdk/web_engine_tester'"
-  (cd "$FLUTTER_DIR/web_sdk/web_engine_tester"; $DART_PATH pub get)
 }
 
 if [[ $KERNEL_NAME == *"Darwin"* ]]

lib/web_ui/dev/felt.bat

@@ -37,13 +37,15 @@ SET DART_BIN=%DART_SDK_DIR%\bin\dart
 
 cd %WEB_UI_DIR%
 
+:: We need to invoke pub get here before we actually invoke felt.
+CALL %DART_BIN% pub get
+
 IF FELT_USE_SNAPSHOT=="0" (
   ECHO Invoking felt.dart without snapshot
   SET FELT_TARGET=%FELT_PATH%
 ) ELSE (
   IF NOT EXIST "%SNAPSHOT_PATH%" (
     ECHO Precompiling felt snapshot
-    CALL %DART_BIN% pub get
     %DART_BIN% --snapshot="%SNAPSHOT_PATH%" --packages="%WEB_UI_DIR%\.dart_tool\package_config.json" %FELT_PATH%
   )
   SET FELT_TARGET=%SNAPSHOT_PATH%

lib/web_ui/dev/steps/compile_tests_step.dart

@@ -441,7 +441,23 @@ Future<void> buildHostPage() async {
     print('Building ${hostDartFile.path}.');
   }
 
-  final int exitCode = await runProcess(
+  int exitCode = await runProcess(
+    environment.dartExecutable,
+    <String>[
+      'pub',
+      'get',
+    ],
+    workingDirectory: environment.webEngineTesterRootDir.path
+  );
+
+  if (exitCode != 0) {
+    throw ToolExit(
+      'Failed to run pub get for web_engine_tester, exit code $exitCode',
+      exitCode: exitCode,
+    );
+  }
+
+  exitCode = await runProcess(
     environment.dartExecutable,
     <String>[
       'compile',