https://www.cloudflare.com/supplemental-terms/
(I'm the lead engineer on Workers. I don't know what happened to OP, though; I'm not personally looped into that conversation.)
Is that at all plausible?
Meanwhile, section "2.8 Limitation on Serving Non-HTML Content" of the terms says: "The Services are offered primarily as a platform to cache and serve web pages and websites. Unless explicitly included as part of a Paid Service purchased by you, you agree to use the Services solely for the purpose of (i) serving web pages as viewed through a web browser or other functionally equivalent applications, including rendering Hypertext Markup Language (HTML) or other functional equivalents, and (ii) serving web APIs subject to the restrictions set forth in this Section 2.8. Use of the Services for serving video or a disproportionate percentage of pictures, audio files, or other non-HTML content is prohibited, unless purchased separately as part of a Paid Service or expressly allowed under our Supplemental Terms for a specific Service. If we determine you have breached this Section 2.8, we may immediately suspend or restrict your use of the Services, or limit End User access to certain of your resources through the Services."
Serving a "disproportionate percentage of [...] non-HTML content is prohibited". To my understanding, that means that web APIs are allowed, but only if they don't return a disproportionate percentage of non-HTML, since the supplemental terms don't expressly allow it (e.g. no JSON-only APIs).