Sub-subdomain Domain name for different environment
Both are completely correct. It can differ organisation by organisation. 
Also, once you start using one of the domain namespace type, you will gradually remember the format and no issues will come. However, I can see one issue here which is related to SSL. 

If you go with any one of the above mentioned namespaces, you need to generate multiple SSL certificates such as *.api.superproduct.com and *.front-end.superproduct.com.

If you go with other namespace type then SSL certs will be required for *.staging.superproduct.com, *.qa.superproduct.com and *.development.superproduct.com.

To avoid this, I would suggest you to have the domains in either of the following formats.


&lt;component-name&gt;-&lt;env-name&gt;.superproduct.com


Examples are:
api-qa.superproduct.com, api-staging.superproduct.com etc.


&lt;env-name&gt;-&lt;component-name&gt;.superproduct.com


Examples are:
qa-api.superproduct.com, staging-api.superproduct.com etc.

In this case, only one SSL certificate for *.superproduct.com will be required.

You can go ahead with the best possible option as per your requirements and analysis.