Hi @zac,
Just to summarize, you're wondering from outside the Azure portal, how can you manage Azure resources associated with your subscription. And if a client id and secret are required for that access, how does one go about creating it. If I have misunderstood in any way, please comment down below.
From a management standpoint, you would go through the management REST APIs, which you can learn more about on the Azure REST API reference documentation. Most services though do support a client SDK providing a native interface for interacting with. However, they do require client authentication with valid credentials.If you're using a client application, you can create an application registration in Microsoft Entra ID for authentication and set the necessary permissions for authorization. The Client Registration section of the reference documentation will walk you through those steps.
I did notice you tagged your question with API Management. In case you question of accessing APIs was referencing that specific service specifically; APIM has a credential manager that you can leverage. You can configure a host of OAuth 2.0 identity providers and create a policy to fetch getting the token. Creating the client and secret would follow the aforementioned client registration section, but the configuration would be slightly different, e.g. the redirects. For those details, check out Create connection to Microsoft Graph API - Azure API Management | Microsoft Learn.