One more account per phone number should be allowed (unless a policy was changed). You can discover if you made that second account using another email authentication by attempting password reset against those emails (login screen, forgot password).
A legacy account, yet never entering API payment method, should be offered only the new system.
Multiple disconnected policies may have been changed around, possibly causing this complication or conflict. A card type or country origin previously eligible for post-payment monthly (arrears billing) may have been disqualified by new payment processor rule settings - by the consideration that less-trustworthy cards could only be used for prepayment. Possible new rules “don’t convert old accounts” due to a flood of problems in doing so, while not considering card restrictions.
One can try more techniques to get to the (undesired) post-payment entrance point. Remove credit cards until nothing on the screen. The old box on the “payment method” would say “add payment method” then, but that’s not what you want now. Log off and back in. Go to the platform.openai.com account main billing category and see if you aren’t offered the “start payment plan” along with an “upgrade” menu button to take you there.