I took the time to compare several third-party apps. I only found one that tracks consent and offers the ability to disable scripts. They claim to be Customer Privacy API compliant.
But according to Cookiebot, we are still not compliant.
What I can gather from Shopify’s own app, based on the reviews, is that it still has some issues to work out. But I am very glad they are working on a native solution.
I also just discovered the Customer Privacy options under Online Store > Preferences.