Zed does have a way to run LLMs without tool calling. From the agent pane, in the menu, select “new text thread”. I believe there’s a keyboard shortcut but I’m on my phone right now.
I couldn't seem to get any message through without tool calling instructions in the payload. What you're describing sounds exactly like what I attempted.
I tried something like over 6 different variations of model configs with restarts of Zed in-between. The documentation and what Zed tries to configure are different as well. The fields don't match up with the built in type checking. I tried "openai" with the endpoint configured, "openai_compatible", and even "openrouter" hoping the REST signatures would be match well enough. Each configured with various fields to turn tool calling off and every single request that hit the REST server had tool calling.
"New text thread" should also have no tools I believe.