I was able to resolve it!
You just need to wait until the final step, when you're ready to file.
At that point, log in through your Fidelity account, look for the Discount page (i.e. Search for "Turbotax Discount") and click "Get Started" with the option "I already have an account in TurboTax".
Then, go directly to the "Order Summary" page, where you'll see the discount applied.
