Thanks for getting in touch! You can see how Octopus connects to your database by checking your connection string. This is located in your OctopusServer.config file (located in C:\Octopus in standard installations), and it is displayed in your Octopus Manager window (see my first screenshot) on your Octopus server.
If your Octopus instance connects to your database via SQL authentication, your connection string will show the username and password. If it's integrated authentication, it won't show username and password in the connection string, and database connections are made by the user that is running your Octopus service. You can find this user by checking the properties of the 'OctopusDeploy' service listed in your services management console (see my second screenshot). If it's running as local system, then the local system account has access to the database.
I hope this helps! Don't hesitate to reach out if you have any further questions or concerns.