Interesting, I am pretty sure the fact that you see iCloud in your Mail settings indicates you have a primary iCloud email address.
Where you see its status as inactive do you have an "Enable this account" checkbox? After you enable it you would likely be able to see your iCloud address. In the image below you would see an "Addresses" list below the "Description" field that would show your iCloud address.
If you cannot enable it or create one, I think your best next step would be to reach out to Apple Support directly. I know you aren't seeing any error but this article seems most relevant to me and contacting them would be the last resort.
If you see a Could Not Create Apple ID or Could Not Set Up iCloud message - Apple Support
"If you see a Could Not Set Up iCloud message
If you see a Could Not Set Up iCloud message, it means that you have exceeded the number of Apple IDs you can set up with iCloud on a single device in one year.
Why did I see this message?
You may see this message when:
- Signing in with an Apple ID you already created on the web, an Apple TV, or a third-party device, but have not yet set up with iCloud
- Signing in with an Apple ID that has web-only access to iCloud
What should you do?
If you have another iPhone, iPad, iPod touch, or Mac, you can try setting up iCloud with your Apple ID on that device. Sign in with your Apple ID, then follow the onscreen steps to start using iCloud.
Or, if you already have an Apple ID set up with iCloud, sign in with that Apple ID instead.
If you still need to set up iCloud with this Apple ID, contact Apple Support for help."
If they have a solution that works, first make sure it is ok to share in the community, then reply to your original question with the solution and mark the reply as helpful or solved. That way others seeing this issue could find it much easier than we could.