etc/webapi.xml
<?xml version="1.0"?>
<routes xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Webapi:etc/webapi.xsd">
<route url="/V1/guest-carts/:cartId/newsletter-subscribe" method="PUT">
<service class="Staempfli\CheckoutNewsletterSubscription\Api\NewsletterSubscriptionManagementInterface" method="subscribe"/>
<resources>
<resource ref="anonymous" />
</resources>
</route>
<route url="/V1/carts/mine/newsletter-subscribe" method="PUT">
<service class="Staempfli\CheckoutNewsletterSubscription\Api\NewsletterSubscriptionManagementInterface" method="subscribe"/>
<resources>
<resource ref="self" />
</resources>
<data>
<parameter name="cartId" force="true">%cart_id%</parameter>
</data>
</route>
</routes>