Apparently there is a Chrome extension that does this.

https://chrome.google.com/webstore/detail/icloud-hide-my-email/omiaekblhgfopjkjnenhahfgcgnbohlk

https://github.com/dedoussis/icloud-hide-my-email-browser-extension/blob/main/src/iCloudClient.ts

Stumbled on this, and someone brought this up to the developer.

https://github.com/dedoussis/icloud-hide-my-email-browser-extension/issues/45

The developer investigated, and the Firefox extension uses the support webextensions API, and it's called but didn't apply the header modifications.

Another link to help, which mide lead way to maybe have this as a native feature.

https://lib.rs/crates/hide_my_email

The gist - Login into icloud.com and use use the auth token to then make calls to icloud.com to manage and create e-mails. This how the plugin above does it, just opens an icloud.com login page in a new tab and grabs the token.

While this library is rust, it could provide the template to building this out native in Orion.