Suppress the autofill password manager after a credential was saved via the API.

chrome/browser/password_manager/chrome_password_manager_client.cc

Index: chrome/browser/password_manager/chrome_password_manager_client.cc
diff --git a/chrome/browser/password_manager/chrome_password_manager_client.cc b/chrome/browser/password_manager/chrome_password_manager_client.cc
index 9264179f4a643aa652b73f99de40c4a9d169b953..f47795c27287cc2b2672bb7392cdb0afe5a44805 100644
--- a/chrome/browser/password_manager/chrome_password_manager_client.cc
+++ b/chrome/browser/password_manager/chrome_password_manager_client.cc
@@ -223,6 +223,10 @@ bool ChromePasswordManagerClient::PromptUserToSaveOrUpdatePassword(
     return false;
   }
 
+  // Prevent the autofill password manager from prompting the second time.
+  if (type == password_manager::CredentialSourceType::CREDENTIAL_SOURCE_API)
+    password_manager_.DropFormManagers();
+
   if (IsTheHotNewBubbleUIEnabled()) {
 #if !BUILDFLAG(ANDROID_JAVA_UI)
     PasswordsClientUIDelegate* manage_passwords_ui_controller =