[codex] Support remote plugin install writes (#18917)

## Summary
- Add a remote plugin install write call that POSTs the selected remote
plugin to the ChatGPT cloud plugin API.
- Align remote install with the latest remote read contract:
`pluginName` carries the backend remote plugin id directly, for example
`plugins~Plugin_linear`, and install no longer synthesizes
`<name>@<marketplace>` ids.
- Validate remote install ids with the same character rules as remote
read, return the same install response shape as local installs, and
include mocked app-server coverage for the write path.

## Validation
- `just fmt`
- `cargo test -p codex-app-server --test all plugin_install`
- `cargo test -p codex-core-plugins`
- `just fix -p codex-app-server`
- `just fix -p codex-core-plugins`

codex-rs/core-plugins/src/remote.rs

@@ -107,6 +107,20 @@ pub enum RemotePluginCatalogError {
         expected_marketplace_name: String,
         actual_marketplace_name: String,
     },
+
+    #[error(
+        "remote plugin install returned unexpected plugin id: expected `{expected}`, got `{actual}`"
+    )]
+    UnexpectedPluginId { expected: String, actual: String },
+
+    #[error(
+        "remote plugin install returned unexpected enabled state for `{plugin_id}`: expected {expected_enabled}, got {actual_enabled}"
+    )]
+    UnexpectedEnabledState {
+        plugin_id: String,
+        expected_enabled: bool,
+        actual_enabled: bool,
+    },
 }
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Deserialize)]
@@ -258,6 +272,12 @@ struct RemotePluginInstalledResponse {
     pagination: RemotePluginPagination,
 }
 
+#[derive(Debug, Clone, PartialEq, Eq, Deserialize)]
+struct RemotePluginInstallResponse {
+    id: String,
+    enabled: bool,
+}
+
 pub async fn fetch_remote_marketplaces(
     config: &RemotePluginServiceConfig,
     auth: Option<&CodexAuth>,
@@ -418,6 +438,41 @@ pub async fn fetch_remote_plugin_detail(
     })
 }
 
+pub async fn install_remote_plugin(
+    config: &RemotePluginServiceConfig,
+    auth: Option<&CodexAuth>,
+    marketplace_name: &str,
+    plugin_id: &str,
+) -> Result<(), RemotePluginCatalogError> {
+    let auth = ensure_chatgpt_auth(auth)?;
+    if RemotePluginScope::from_marketplace_name(marketplace_name).is_none() {
+        return Err(RemotePluginCatalogError::UnknownMarketplace {
+            marketplace_name: marketplace_name.to_string(),
+        });
+    }
+
+    let base_url = config.chatgpt_base_url.trim_end_matches('/');
+    let url = format!("{base_url}/ps/plugins/{plugin_id}/install");
+    let client = build_reqwest_client();
+    let request = authenticated_request(client.post(&url), auth)?;
+    let response: RemotePluginInstallResponse = send_and_decode(request, &url).await?;
+    if response.id != plugin_id {
+        return Err(RemotePluginCatalogError::UnexpectedPluginId {
+            expected: plugin_id.to_string(),
+            actual: response.id,
+        });
+    }
+    if !response.enabled {
+        return Err(RemotePluginCatalogError::UnexpectedEnabledState {
+            plugin_id: plugin_id.to_string(),
+            expected_enabled: true,
+            actual_enabled: response.enabled,
+        });
+    }
+
+    Ok(())
+}
+
 fn build_remote_plugin_summary(
     plugin: &RemotePluginDirectoryItem,
     installed_plugin: Option<&RemotePluginInstalledItem>,