chore: change built_in_model_providers so "openai" is the only "bundled" provider (#1407)

As we are [close to releasing the Rust CLI
beta](https://github.com/openai/codex/discussions/1405), for the moment,
let's take a more neutral stance on what it takes to be a "built-in"
provider.

* For example, there seems to be a discrepancy around what the "right"
configuration for Gemini is: https://github.com/openai/codex/pull/881
* And while the current list of "built-in" providers are all arguably
"well-known" names, this raises a question of what to do about
potentially less familiar providers, such as
https://github.com/openai/codex/pull/1142. Do we just accept every pull
request like this, or is there some criteria a provider has to meet to
"qualify" to be bundled with Codex CLI?

I think that if we can establish clear ground rules for being a built-in
provider, then we can bring this back. But until then, I would rather
take a minimalist approach because if we decided to reverse our position
later, it would break folks who were depending on the presence of the
built-in providers.

codex-rs/core/src/model_provider_info.rs

@@ -83,6 +83,10 @@ impl ModelProviderInfo {
 pub fn built_in_model_providers() -> HashMap<String, ModelProviderInfo> {
     use ModelProviderInfo as P;
 
+    // We do not want to be in the business of adjucating which third-party
+    // providers are bundled with Codex CLI, so we only include the OpenAI
+    // provider by default. Users are encouraged to add to `model_providers`
+    // in config.toml to add their own providers.
     [
         (
             "openai",
@@ -94,76 +98,6 @@ pub fn built_in_model_providers() -> HashMap<String, ModelProviderInfo> {
                 wire_api: WireApi::Responses,
             },
         ),
-        (
-            "openrouter",
-            P {
-                name: "OpenRouter".into(),
-                base_url: "https://openrouter.ai/api/v1".into(),
-                env_key: Some("OPENROUTER_API_KEY".into()),
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
-        (
-            "gemini",
-            P {
-                name: "Gemini".into(),
-                base_url: "https://generativelanguage.googleapis.com/v1beta/openai".into(),
-                env_key: Some("GEMINI_API_KEY".into()),
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
-        (
-            "ollama",
-            P {
-                name: "Ollama".into(),
-                base_url: "http://localhost:11434/v1".into(),
-                env_key: None,
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
-        (
-            "mistral",
-            P {
-                name: "Mistral".into(),
-                base_url: "https://api.mistral.ai/v1".into(),
-                env_key: Some("MISTRAL_API_KEY".into()),
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
-        (
-            "deepseek",
-            P {
-                name: "DeepSeek".into(),
-                base_url: "https://api.deepseek.com".into(),
-                env_key: Some("DEEPSEEK_API_KEY".into()),
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
-        (
-            "xai",
-            P {
-                name: "xAI".into(),
-                base_url: "https://api.x.ai/v1".into(),
-                env_key: Some("XAI_API_KEY".into()),
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
-        (
-            "groq",
-            P {
-                name: "Groq".into(),
-                base_url: "https://api.groq.com/openai/v1".into(),
-                env_key: Some("GROQ_API_KEY".into()),
-                env_key_instructions: None,
-                wire_api: WireApi::Chat,
-            },
-        ),
     ]
     .into_iter()
     .map(|(k, v)| (k.to_string(), v))