Update models to match new OpenAI's API identifiers

[Kumala3]

Hello,
I wanted to test out this project by using OpenAI models and run into technical issues with from what I understood incorrect identifiers or maybe even something more serious. Whenever I typed any message and sent it using GUI I got this error

 POST /api/chat 500 in 830ms
 ⨯ AI_APICallError: Project `proj_theq_example123` does not have access to model `gpt-4o`
    at D:\Kostek\Projects\open-deep-research\.next\server\chunks\node_modules__pnpm_89496e._.js:9272:24
    at async postToApi (D:\Kostek\Projects\open-deep-research\.next\server\chunks\node_modules__pnpm_89496e._.js:9179:36)
    at async OpenAIChatLanguageModel.doGenerate (D:\Kostek\Projects\open-deep-research\.next\server\chunks\node_modules__pnpm_89496e._.js:10744:54)
    at async fn (D:\Kostek\Projects\open-deep-research\.next\server\chunks\6a7be_ai_dist_index_mjs_4d9bd4._.js:3737:44)
    at async D:\Kostek\Projects\open-deep-research\.next\server\chunks\6a7be_ai_dist_index_mjs_4d9bd4._.js:441:28
    at async _retryWithExponentialBackoff (D:\Kostek\Projects\open-deep-research\.next\server\chunks\6a7be_ai_dist_index_mjs_4d9bd4._.js:266:16)
    at async fn (D:\Kostek\Projects\open-deep-research\.next\server\chunks\6a7be_ai_dist_index_mjs_4d9bd4._.js:3696:40)
    at async D:\Kostek\Projects\open-deep-research\.next\server\chunks\6a7be_ai_dist_index_mjs_4d9bd4._.js:441:28
    at async generateTitleFromUserMessage (D:\Kostek\Projects\open-deep-research\.next\server\chunks\[root of the server]__0fc243._.js:1061:29)
    at async POST (D:\Kostek\Projects\open-deep-research\.next\server\chunks\[root of the server]__0fc243._.js:1311:23)

I understand that the error is saying that the project doesn't have access to the specific model, however, I have this model allowed in the project, double-checked it and updated the key 2 times -> it still doesn't work. Therefore, I suppose that there's an error in the technical part.

Moreover, it's very confusing on how to select a reasoning model and to USE IT for the query. Additionally, there are new reasoning models from OpenAI dropped (o4-mini)

I would appreciate if the development team could take my suggestions into consideration and I would like to contribute into the project development as I am studying it at the moment