I got a response from Apple Support, they confirm that indeed there is no such API method. Here's the relevant part of their response for posterity and clarity:

You are correct that the App Store Connect API doesn't provide a direct method to add a device to an existing provisioning profile. To include a new device, you need to create a new provisioning profile that incorporates the desired devices. This process involves deleting the existing profile and generating a new one with the updated device list.