As far as I know, the Version Control Private Server (SVN) connection in Mendix Studio Pro works only with basic authentication (username/password). This conclusion is based on the fact that Studio Pro does not offer any other authentication options in the UI, and the official documentation does not mention support for PAT tokens, Kerberos, SSH keys, or browser-based SSO for SVN connections. The Mendix documentation consistently describes SVN usage with username/password and does not reference alternative authentication mechanisms.
References that support this understanding:
https://docs.mendix.com/refguide10/version-control/
https://docs.mendix.com/refguide10/on-premises-git/