[logging] Use PluginLogger for bazel doctor and analytics (flutter#8373)

I'm just looking through the code and checking that paths aren't going
to be logged. Bazel path for flutter doctor probably is used very little
(if at all) and analytics isn't used at all (will probably be moved to
dart plugin?).

Related to flutter#8369

Author: helin24

src/io/flutter/actions/FlutterDoctorAction.java

@@ -16,6 +16,7 @@
 import io.flutter.FlutterUtils;
 import io.flutter.bazel.Workspace;
 import io.flutter.console.FlutterConsoles;
+import io.flutter.logging.PluginLogger;
 import io.flutter.pub.PubRoot;
 import io.flutter.sdk.FlutterSdk;
 import org.jetbrains.annotations.NotNull;
@@ -25,7 +26,7 @@
 
 public class FlutterDoctorAction extends FlutterSdkAction {
 
-  private static final @NotNull Logger LOG = Logger.getInstance(FlutterDoctorAction.class);
+  private static final @NotNull Logger LOG = PluginLogger.createLogger(FlutterDoctorAction.class);
 
   public void startCommand(@NotNull Project project, @NotNull FlutterSdk sdk, @Nullable PubRoot root) {
     sdk.flutterDoctor().startInConsole(project);

src/io/flutter/analytics/UnifiedAnalytics.java

@@ -17,6 +17,7 @@
 import com.jetbrains.lang.dart.ide.toolingDaemon.DartToolingDaemonService;
 import de.roderick.weberknecht.WebSocketException;
 import io.flutter.dart.DtdUtils;
+import io.flutter.logging.PluginLogger;
 import io.flutter.sdk.FlutterSdkUtil;
 import io.flutter.utils.OpenApiUtils;
 import org.jetbrains.annotations.NotNull;
@@ -28,7 +29,7 @@
  * Facilitates sending information to unified analytics.
  */
 public class UnifiedAnalytics {
-  private static final @NotNull Logger LOG = Logger.getInstance(UnifiedAnalytics.class);
+  private static final @NotNull Logger LOG = PluginLogger.createLogger(UnifiedAnalytics.class);
 
   @Nullable Boolean enabled = null;
   final Project project;