The question was interpreted as “why do admin tools have these features” on account of that was in the first sentence, and not, as you may have imagined, a request for a twitter employee to explain all of their tools, or a request for a twitter employee to justify creating these tools.

it's not copying the cookie, but there are absolutely third party UIs via a user's API key, it's not a huge leap of faith to assume Twitter has similar internally.

A tool that allows an employee to access a user's API key? That sounds like a bad idea, especially if that tool is accessible to support personnel.