Update to new agent schema (#35578)

Release Notes:

- N/A

---------

Co-authored-by: Agus Zubiaga <agus@zed.dev>

crates/agent_servers/src/settings.rs

@@ -13,7 +13,6 @@ pub fn init(cx: &mut App) {
 pub struct AllAgentServersSettings {
     pub gemini: Option<AgentServerSettings>,
     pub claude: Option<AgentServerSettings>,
-    pub codex: Option<AgentServerSettings>,
 }
 
 #[derive(Deserialize, Serialize, Clone, JsonSchema, Debug)]
@@ -30,21 +29,13 @@ impl settings::Settings for AllAgentServersSettings {
     fn load(sources: SettingsSources<Self::FileContent>, _: &mut App) -> Result<Self> {
         let mut settings = AllAgentServersSettings::default();
 
-        for AllAgentServersSettings {
-            gemini,
-            claude,
-            codex,
-        } in sources.defaults_and_customizations()
-        {
+        for AllAgentServersSettings { gemini, claude } in sources.defaults_and_customizations() {
             if gemini.is_some() {
                 settings.gemini = gemini.clone();
             }
             if claude.is_some() {
                 settings.claude = claude.clone();
             }
-            if codex.is_some() {
-                settings.codex = codex.clone();
-            }
         }
 
         Ok(settings)