Rules that look right in the app but do nothing in checkout almost always come down to one of five things. Test in your own checkout after each change.
Open Shopify Checkout → Rules. If you see the banner COD in Checkout is disabled with the text "Rules are saved but do not apply. Enable the feature in the Activation tab", that is your answer. The banner Setup required means the shipping rate or the payment method has not been chosen yet.
The app finds your COD delivery option by its exact name. Rename the rate in Shopify, even by one character, and the app no longer recognises it. After any change to your shipping rates, go back to Activation and select the rate again.
The same applies to the manual Cash on Delivery payment method. If it has been renamed or deactivated, the app cannot find it and leaves checkout untouched. Reactivate it, then reselect it under Select payment method.
Activating the feature creates two entries in your Shopify settings, Customize available payment methods based on selected shipping and Customize available delivery methods based on selected payment. If either is switched off, the rules stop working. Switch them back on.
On Free and Basic only one rule is used, so a second and third rule are ignored in checkout with no message. The banner Rule limit on the Rules page says so. Separately, once you pass your monthly COD order limit, the COD form stops for customers and the checkout half changes rather than stops. The link between the shipping rate and the payment method stops being enforced, so Cash on Delivery becomes payable on every rate. Your delivery rules keep running, so the COD rate stays hidden wherever you told it to be. Upgrade, or wait for the month to roll over.
Remember that local delivery and store pickup are deliberately left alone, so their payment options do not change.
After any fix, place a test order through checkout with a matching cart and a non-matching one.
Stuck on any of this? Open the chat in the bottom right corner of the app and we will help you set it up.