The previous API system allowed you to have your friends give you an API key for their account that you could use in, let’s say pyfa, to offer them help with things - without requiring them to log into their account on your machine. It seems like ESI doesn’t offer any way to handle that - did the EVE devs really downgrade us? Just coming back after years away…
That functionality indeed no longer exists.
You can share refresh tokens just like you used to share API keys.