As another follow up, I believe I’ve tracked this down to a conflict with the WordFence security/firewall plugin. WordFence applies Recaptcha v3 to globally to the site, but the Coupon Affiliates plugin only uses v2. I disabled Recaptcha v2 in the Coupon Affiliates settings, but I am still getting the error.
After some additional research I found that this issue was supposedly fixed in Version 4.16.2. However, it is still not working for me.
Updates | Coupon Affiliates