Your Nathean Analytics credentials get saved by Power BI when you logon for the first time. Power BI identifies a data source using a combination of its Kind and Path. When a data source is encountered during a query evaluation, the M engine will try to find matching credentials. If no credentials are found, the engine returns an special error that results in a credential prompt in Power Query.
You can see an example of how credentials are stored in the Data source settings dialog in Power BI Desktop. In this dialog, the Kind is represented by an icon, and the Path value is displayed as text.
And when you logon to Nathean Analytics from Power BI you are presented with the following dialog
If you connect to multiple different instances of Nathean Analytics and connect to those via Power BI, then Power BI will save multiple sets of credentials. The unique key for each is the Nathean Analytics URL and the System Code of the Tenant.