It sounds to me like the tier didn’t fullly upgrade from “free”, and you just have the limited free trial model.
Here is the place to check your tier level, with it showing alongside the page header, and also in a center graph that has a green color bar that grows.
https://platform.openai.com/settings/organization/limits
Free tier still will have significant limits and limited models when you expand “all models”, such as 3 RPM, 50 RPD all over the place, on models that should be unable to be called if you have no credits purchased ever.
You can ensure you have selected the correct organization that made the purchase, lower-left, and the default project of that org, upper-left in the platform site.
If you have your paid balance showing in the selected organization under “billing”, and you have that line item of the payment under “credit grants”, then there is nothing that should stop you from using the majority of OpenAI models. The exact gating of API features and models by ID verification (plus video selfie facial recognition), such as not being able to use gpt-image generation or streaming responses, was a help page now removed. You may need to hard-refresh the platform site (ctrl-refresh, shift-refresh,…) if you’ve had any page constantly open since making the payment.
I have my own “playground” site that will take an API key, and make direct calls to OpenAI. It doesn’t use any server resources, and will store data in your browser’s local storage. It doesn’t deny you attempts based on some separate “did they pay” backend API. It has a “refresh models” button upper right next to model selection so you can see what model IDs your org can call, an API call you can make for free, and you can see any error you get making calls to “chat” against a variety of API models when you send messages. The page does not stream so as to not to trigger any additional ID verification gates.
If an issue persists for you, you can either pay in another $5, and see if that causes a proper re-trigger, or contact OpenAI support via help.openai.com for proper tier provisioning, and wait quite a while.