Replace zed_llm_client with cloud_llm_client (#35309)

This PR replaces the usage of the `zed_llm_client` with the
`cloud_llm_client`.

It was ported into this repo in #35307.

Release Notes:

- N/A

crates/web_search/Cargo.toml

@@ -13,8 +13,8 @@ path = "src/web_search.rs"
 
 [dependencies]
 anyhow.workspace = true
+cloud_llm_client.workspace = true
 collections.workspace = true
 gpui.workspace = true
 serde.workspace = true
 workspace-hack.workspace = true
-zed_llm_client.workspace = true

crates/web_search/src/web_search.rs

@@ -1,8 +1,9 @@
+use std::sync::Arc;
+
 use anyhow::Result;
+use cloud_llm_client::WebSearchResponse;
 use collections::HashMap;
 use gpui::{App, AppContext as _, Context, Entity, Global, SharedString, Task};
-use std::sync::Arc;
-use zed_llm_client::WebSearchResponse;
 
 pub fn init(cx: &mut App) {
     let registry = cx.new(|_cx| WebSearchRegistry::default());