Julie here from Shopify Support.
You're right — in order to use the Parcelify app, you must have the Carrier Calculated Shipping feature enabled on your Shopify plan. This feature can be added in a few different ways; it's included in the Advanced plan, and you can also add it to any plan for an additional $20 USD per month. If you switch to annual billing, then the Carrier Calculated Shipping feature can be added to your plan for free.
I'm glad to hear that you're already on an annual billing cycle. To have this feature enabled, you'll just need to contact Support directly. Through an authenticated live chat, they'll be able to access your account and activate the feature for you.
I hope this helps!