Same issue seems to be happening as far as 12th November 2021.
1.Unable to receive authentication emails from EA Origin when i'm looking to turn on "Login Verification" - am prompted that a verification code will be sent to my registered email.
2. Spoke to an EA advisor which provided the solution to "Please try to enable your login verification in EA account, refer to this link in order to understand the steps to update Login verification: https://help.ea.com/en/help/account/ea-login-verification-information/ "
3. Repeat step 1.
Similar to OP - They were able to send me validation emails for the support chat and the case details email but still the Verification Email process/server is not issues the one email that I actually need.
Finally the EA advisor had indicated it 'can be' an issue with the service provider as sometime that is not in the sync which delays the mails.
/tldr - EA Origin is not sending its verification emails to verify me so that i can enable verification emails to be sent to me.
Any solutions other then to wait? Between OP's posting date in Feburary till date it seems to remain unsolved.