Connecting a google cloud project to a programmable search engine?

[sbraun]

GOAL: I want to set up a billing account with my programmable search engine so I can do more than 100 search queries a day.

SITUATION: I currently have an instance of the programmable search engine (Image 1) and a google cloud project with the Custom Search API enabled (Image 2) and a billing account attached to it. How can I link the two so I can use my programmable search engine instance and be billed on my google cloud project? Thanks for any help!

WHAT I'VE FOUND: On this website: https://developers.google.com/custom-search/docs/paid_element, it says what shows on (Image 3). But the billing link goes to a generic "how to setup billing" page that doesn't make mention on how to actually link the programmable engine and the google cloud project (https://cloud.google.com/billing/docs/how-to/manage-billing-account).

[Image 1]: https://i.sstatic.net/OwnPsu18.png
[Image 2]: https://i.sstatic.net/ZzjHc0mS.png
[Image 3]: https://i.sstatic.net/fHqab76t.png