I believe you are prohibited from this operation that used to be possible like 10 years ago iirc (OP answered it wasn’t possible, but a comment on the answer reported success and some screen shots from 2023 timeframe).
Before attempting this I would recommend opening a case with Apple support to get in writing that they support the proposed swap. Some report permanent locks on using an external to Apple email when attempting this. My hunch is they won’t allow this as it’s not possible (economical) for them to rule out some malicious takeovers and they choose to take the heat from people wanting to reuse an email and not the heat from people who lose an account when this happens without consent.
In your case, open a support so Apple can advise in your specific case. Apple ID are not all created the same and perhaps you qualify for a different treatment than one created as a stand alone ID.
The special cases include when an Apple ID is associated with Apple Developer and legal contracts have been signed. Work or school managed, related or generated Apple ID, parental and minor related ID with family sharing.
Even deleting your Apple ID prevents reuse of the old email.
Can I use the primary email address for my deleted Apple ID account to create a new Apple ID or with another existing Apple ID account?
No, once your Apple ID is deleted, you can't use the email address that you used with it to create a new Apple ID. In addition, you can't use that email address with another existing Apple ID except as a rescue email. Also, if your primary Apple ID email address is with a Custom Email Domain, it can never be reused to create an Apple ID after your Apple ID is deleted, even if the domain ownership changes.