I mean the OpenAI API integration but on a different hostname, like another URL that is OpenAI compatible, not with another ACP following agent framework.

Try this in Zed:

Open settings > AI > LLM Providers [Configure] >

there is OpenAI and OpenAI subscription - ignore those two.

On top-right, there is "Add Provider" with two options:

1. Compatible APIs (OpenAI)

2. Compatible APIs (Anthropic)

When I choose "Compatible APIs (OpenAI)", I can input a custom API URL.