this apple id is deleted a month or two ago
Deleted, and no longer available. It may still be a valid email address from another service provider, for example an @gmail.com address, but for identification purposes on an Apple ID it is not available because Apple IDs must be unique.
Note, too from Apple's support page How to deactivate your Apple ID account under the paragraph About deactivating your Apple ID:
When you deactivate your Apple ID account, we keep your account and data intact, but you can't sign in to your account or use it. While your account is deactivated, you can't access data that you stored with Apple services that use your Apple ID, such as iCloud, iTunes, Apple Books, the App Store, Apple Pay, iMessage, FaceTime, and Find My iPhone. Apple stops processing or accessing your data, except where we are under an obligation to use it for another lawful purpose such as financial returns or other legal procedure.
...since it is used with an apple id.
This means that although your account has been terminated, Apple is obliged to retain some data for legal reasons and this includes your Apple ID information. This makes it unavailable to be used again on a new Apple ID account.