I used to have 2 Apple IDs and I have since deleted 1. The issue I’m having is that the old Apple ID is still logged in to the iCloud and won’t allow me to log it out so I can change it to the other Apple ID. Is there anything I can do for this?

No, there is no fix for that. Apple cannot do anything either. It is imperative that when deleting an AppleID, it must be signed out on your devices before Apple processes the deletion request. After it is deleted, if still signed in it cannot be signed out, ever.

This is explained at least twice that I know of when going through the process of requesting an AppleID be deleted.

See -> How to delete your Apple ID account - Apple Support

• “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.“

As I said, and as evident from numerous posts here, that won’t change anything. Once the AppleID is deleted from Apple’s system, there is no way for even Apple to disassociate it from a device that was signed in once the deletion request was processed and finalized.

As I said, and as explained multiple times in forms and emails to people filling in and requesting an AppleID be deleted, signing the AppleID out on all devices before it is finally deleted is critical. Once that AppleID is deleted, there is no solution for devices that were not already signed out.

Since that Apple ID is deleted your option now is to get proof of purchase then contact Apple to request iCloud be removed from their end with that proof.