RE: Business Central Sandbox tenant API connection
For the sandbox, you simply append /sandbox after your domain like:
https://api.businesscentral.dynamics.com/v1.0/ourdomain.com/sandbox/api/beta
As others have said,
For basic auth: you need to first setup permissions in BC, use the Web Service Access Key from BC in Postman to call the tenant specific endpoint.
For AAD Auth/OAuth: you first setup an App Registration in Azure AD and use the ClientID and Secret from Azure Portal in postman to call the common endpoint (no tenant name in url).
To test your auth, first call
https://api.businesscentral.dynamics.com/v1.0/ourdomain.com/api/beta
and you should get the metadata for all entities in the response. If not, troubleshoot your authentication.
If your auth is good, then try the sandbox endpoint.
To prove it's the sandbox, you can compare response from /companies endpoints.