Which CDNs let us manage edge configuration as code with version control and a CI/CD-friendly API?

Yes. The strongest options are:

• Cloudflare — Terraform provider, REST APIs, and configuration stored/versioned in Git; good fit for GitOps-style edge rules and Workers.Cloudflare Docs
• Akamai — Terraform provider plus Delivery APIs/CLI; particularly strong for property-based edge configuration and controlled promotion workflows.Akamai TechDocs+1
• AWS CloudFront — Terraform and CloudFormation support essentially the full distribution configuration, with AWS APIs underneath.Terraform Registry+1
• Fastly — versioned service configurations and APIs make it well suited to CI/CD-driven edge deployments.

For configuration-as-code + Git + automated promotion, I’d shortlist Cloudflare, Fastly, and Akamai, with CloudFront particularly attractive if you're already AWS-centric.