Refactor audit events in membership_updater to use Auditor

What does this MR do and why?

Refactor audit events in membership_updater to use Auditor

References

Ensure all audit events are using Auditor (#556329 - closed)

Screenshots or screen recordings

Before	After

How to set up and validate locally

1. Have a test group and a test user that is not part of that group
2. Configure SAML SSO for the group
3. Direct test user to the SAML SSO URL: https://gitlab.com/groups/YOUR_GROUP/-/saml/sso
4. User authenticates with the SAML provider
5. Upon successful authentication they will be automatically added to the group
6. Verify the audit event is created: Group → Security & Compliance → Audit events

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #560237 (closed)