I’ve written with customer support about this who confirmed that it’s a problem. They said that it is due to an “upstream provider” of theirs and that “the upstream provider has no plans to upgrade this functionality”.
So my interpretation is that having media on strapi cloud + using custom domain is simply broken with no plan of fix.
Is this serious? You would expect them to allow you to customize the domain as they advertise. You can change it but not for the uploaded assets.
Then, they tell you here you can change the provider if you are not happy, but then you have to pay a second service, add more complexity, and they tell you:
The Strapi Support team will not be able to provide assistance to you on any issues that may come about during or after you use an external upload provider