GPT-5 web search (if that is possible)

I don’t know if it’s a bug, potential oversight, or just not possible, but all the new GPT-5 models have web search, but the “normal” GPT-5 does not for some reason.

I thought the way all models have web search, always makes it possible, that’s why I’m confused.

Please let me know, if it’s coming, or if the model / API does not allow for it.