If this was a child account, deleting it doesn’t remove it from Family Sharing immediately. Apple says the account deletion has to fully take effect before the organizer can remove the child.
I’d check the September 23 email carefully to see whether it confirms the deletion request or says the account has actually been deleted. Apple notes that deletion can take some time to process.
Once the deletion is complete, try Settings > Family > your son’s name again. If the account still appears and there’s no option to remove it, I’d contact Apple Support rather than making more account changes.
Also, a deleted Apple Account can’t be transferred to the new family. You’ll need to use/create an account for him in the new Family Sharing group.