Expose environment status through app-server (#32920)

## What changed

- Add the experimental `environment/status` request for inspecting a configured environment without starting or reconnecting it.
- Report `ready`, `pending`, `disconnected`, or `unknown`, including error details for disconnected and unknown environments.
- Probe ready remote environments over their existing exec-server connection.

## Testing

- Add an app-server integration test covering local and remote ready, pending, disconnected, and unknown environments.

GitOrigin-RevId: 397bba603aa9e0b59008ee6cb7cbde46e357652c

codex-rs/app-server-protocol/src/protocol/v2/environment.rs

@@ -37,6 +37,51 @@ pub struct EnvironmentInfoResponse {
     pub cwd: Option<PathUri>,
 }
 
+/// Parameters for reading the current status of one configured environment.
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct EnvironmentStatusParams {
+    /// Environment id to inspect.
+    pub environment_id: String,
+}
+
+/// Current status for the requested environment.
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
+pub struct EnvironmentStatusResponse {
+    /// Current status observed without starting or recovering the environment.
+    pub status: EnvironmentStatusKind,
+    /// Human-readable detail for `disconnected` and `unknown`; omitted for other statuses.
+    #[serde(default, skip_serializing_if = "Option::is_none")]
+    #[ts(optional)]
+    pub error: Option<String>,
+}
+
+/// Current status observed by app-server without starting or recovering an environment.
+///
+/// For a currently ready remote environment, app-server asks the existing
+/// exec-server connection for `environment/status` without allowing recovery.
+#[derive(Serialize, Deserialize, Debug, Clone, Copy, PartialEq, Eq, JsonSchema, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(rename_all = "camelCase", export_to = "v2/")]
+pub enum EnvironmentStatusKind {
+    /// The environment is local, or an already-connected remote exec-server answered
+    /// `environment/status` over its existing initialized connection.
+    Ready,
+    /// The configured environment has no ready connection and no observed connection failure.
+    /// This includes lazy environments that have never been started and initial startup that has
+    /// not finished.
+    Pending,
+    /// A connection attempt, prior connection, or fail-fast `environment/status` probe observed
+    /// a failure. This does not promise the failure is terminal: later normal environment use may
+    /// recover it. This call does not trigger recovery; `error` contains the observed reason.
+    Disconnected,
+    /// The requested environment id is not configured in app-server.
+    Unknown,
+}
+
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]