The $20/mo plus only gets you features that you can access in the web interface. It is independent from the API usage that bills by the query. Anything you can get from the API, you can get without paying for plus.
There have been addons that were able to use the web interface to get authorization (ex: ChatGPT4Google). I was hoping some similar session authentication and cache and make them available in terminal
Can't access the GPT-4 model through the API yet
Maybe you already did that, just reminder for those who don't know - you need to apply for API access for gpt-4. I did that and was granted it after about 2 days.