I am utilizing Cloudflare for a public website. Recently, I have been adjusting many different configuration values via the website/UI. Is there a way to download/upload the configuration so that it can be version-controlled?
You can configure Cloudflare using Terraform. Check out Terraform Cloudflare Provider here.
You can use a tool called cf-terraforming delivered by Cloudflare that allows to download the Cloudflare setup into Terraform.