Can I use Magical Fees in a Hydrogen or headless storefront?

Yes. The easiest way is the Everywhere Method, available on every plan including Starter. Everywhere fees are added automatically by Shopify at checkout, so they work with your headless cart and checkout. No theme code or app blocks required. Create a fee using one of the conditions (product tag, collection, specific products, product type, or storefront country) and it applies automatically.
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If you are on Shopify Plus, the checkout UI extension is also a great option, and it is the one to choose when your fee needs conditions the Everywhere Method does not support, such as payment method or customer tags. Note: with either approach, fee information is not displayed on the product or cart pages of a headless store; buyers first see the fee at checkout.