In your operating system's credential store, on your machine. When you connect a platform, you sign in with that platform's own login, such as OAuth for Databricks. The token that comes back is kept locally and not sent to Emolysis.
Emolysis's services never connect to your data platform, so they have no use for your platform credentials. Your own model key, on any plan, is kept the same way.
Emolysis acts on your platform only through these local credentials, with your account's permissions, so what it can do there is limited to what your account can do. Credentials are never written into a project folder or committed to your repository. See connecting Databricks and the security page.