fix: show correct Bedrock runtime endpoint in /status (#20275)

## Why

`/status` was showing the configured `ModelProviderInfo.base_url` for
Amazon Bedrock, which can be stale or misleading because the actual
Bedrock Mantle endpoint is derived at runtime from the resolved AWS
region. This made sessions report the wrong provider endpoint even
though requests used the correct runtime URL.

## What changed

- Added `ModelProvider::runtime_base_url()` so provider implementations
can expose the request-time base URL through the shared runtime provider
abstraction.
- Moved Bedrock region-to-Mantle URL resolution into
`amazon_bedrock::mantle::runtime_base_url()`, keeping region resolution
private to the Mantle module.
- Overrode `runtime_base_url()` for Amazon Bedrock so it returns the
resolved Mantle endpoint instead of the configured default.
- Resolved and cached the runtime provider base URL during TUI startup,
then used that cached value when rendering `/status`.
- Added status coverage that verifies Bedrock displays the runtime URL
and ignores the configured Bedrock `base_url` when they differ.

## Verification
model provider is resolved correctly in local build:
<img width="696" height="245" alt="Screenshot 2026-04-29 at 5 01 36 PM"
src="https://github.com/user-attachments/assets/a13c10a5-3720-41ab-8ace-3c4bc573f971"
/>

codex-rs/model-provider/src/provider.rs

@@ -106,6 +106,11 @@ pub trait ModelProvider: fmt::Debug + Send + Sync {
             .to_api_provider(auth.as_ref().map(CodexAuth::auth_mode))
     }
 
+    /// Returns the provider base URL that will be used at request time.
+    async fn runtime_base_url(&self) -> codex_protocol::error::Result<Option<String>> {
+        Ok(self.info().base_url.clone())
+    }
+
     /// Returns the auth provider used to attach request credentials.
     async fn api_auth(&self) -> codex_protocol::error::Result<SharedAuthProvider> {
         let auth = self.auth().await;
@@ -333,6 +338,22 @@ mod tests {
         assert_eq!(provider.capabilities(), ProviderCapabilities::default());
     }
 
+    #[tokio::test]
+    async fn configured_provider_runtime_base_url_uses_configured_base_url() {
+        let provider = create_model_provider(
+            provider_for("https://example.test/v1".to_string()),
+            /*auth_manager*/ None,
+        );
+
+        assert_eq!(
+            provider
+                .runtime_base_url()
+                .await
+                .expect("runtime base URL should resolve"),
+            Some("https://example.test/v1".to_string())
+        );
+    }
+
     #[test]
     fn create_model_provider_builds_command_auth_manager_without_base_manager() {
         let provider = create_model_provider(