Yes, FusionAuth provides this information via the authenticationType claim in the JWT. This claim indicates the authentication method used, such as PASSWORD, GOOGLE, SAML, etc.
How to Access Authentication Type:
From the JWT: The authenticationType claim is included in the JWT access token. Documentation: JWT Access Token Claims From a Webhook Event (Alternative Approach): The same authenticationType value is included in the user.login.success webhook event. This may be useful if your system processes authentication events via webhooks instead of decoding JWTs. Documentation: User Login Success WebhookFor additional details on JWT structure and claims, refer to: JWT Components Explained