How can I delete an Apple ID that no longer exists?

You were instructed to sign out from that Apple ID on all devices before you requested Apple delete it from their end. Since you didn’t, the only way to do it now is to submit proof of ownership and request Apple remove the Apple ID from the device for you. See “Start a support request“ at How to remove Activation Lock - Apple Support

For information about how to delete an Apple ID account, read this support article —> How to delete your Apple ID account - Apple Support

Carefully and thoroughly read that article for information about what happens when you delete your Apple ID account. For example:

"Make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted."

From: How to delete your Apple ID account - Apple Support

"What happens if I change my mind after I have requested that my account be deleted?

While your request is being processed, you can contact Apple Support [call them at a telephone number for your country --> Contact Apple for support and service - Apple Support ] with the unique alphanumeric access code you received, and we’ll help you cancel your request. After your account is deleted, Apple can't cancel the request, reopen your account, or restore your data."

Apple can reset a device if a person can provide sufficient evidence of valid ownership (usually the original receipt from Apple or an authorized retailer —> Keep your receipt after you buy an Apple device - Apple Support ). Try this online here --> https://al-support.apple.com/#/additional-support (Yes, apparently this does work in this situation too: How to remove previously deleted apple id… - Apple Community )

I've experienced this issue as well, and I found a solution that worked for me: updating my iOS software. It's interesting to note that this type of problem can also occur with other platforms, such as Microsoft and Google. When you encounter such difficulties, one of the first steps I recommend is to check for any available updates for your iOS software.

Sometimes, a simple update can resolve various bugs and improve performance significantly. If, after checking, you find that there are no updates available, or if updating doesn’t solve the problem, it may be helpful to just give it some time. Technical glitches can sometimes resolve themselves after a brief pause.

If you have any further questions or if there's anything else you'd like to discuss, please don't hesitate to ask! And remember, patience truly is a virtue when dealing with technology—sometimes the best solution is to step away and let things settle for a moment.