There have been posts by people who have contacted Apple Support and they were told that if you delete an ID associated with an email address, you can never reuse the email address for an Apple ID. I have also seen posts that stated Apple told them there was a 30 day waiting period before the address could be used again.You will need to get another e-mail address to use as your Apple ID or you can try waiting 30 days to see if that works.
There is only one @iCloud account associated with your Apple ID. You have to use that address. You can't use an iCloud alias address as your Apple ID email address.
Based on what I have read, I suggest you leave your Apple ID email address as a 3rd party email address because you have more flexibility if you need to change the email address. For example, if the Apple ID got compromised, you can change it to another address. I also have read of many people who were locked out of their accounts when they forgot their password. Since the recovery email address is the @iCloud email address, if you forget your password, you also can't access your email to get emails from Apple to recover your account. You can set a rescue email address, but for some people, this hasn't worked.