I appreciate your candor related to the docs. We do know that we need to make the docs more approachable for beginners, especially when it comes to authentication. This is something that we are actively thinking about.
Just to clarify your ask, I believe that you are trying to authorize your existing application to be able to make requests on behalf of other @handles. Please correct me if I’m wrong.
If this is the case, you are going to have to use the ‘Sign in with Twitter’ feature. Here is a good guide for implementing this tool:
https://developer.twitter.com/en/docs/twitter-for-websites/log-in-with-twitter/guides/implementing-sign-in-with-twitter
It is, admittedly, not the easiest thing to implement, but it is the best way for you to pull the proper tokens to make a request on behalf of another @handle.
Please let me know if you have any questions about this.