[profile-switcher][rust] -- [1/2] Add app-server account session protocol (#25469)

## Summary

Adds the app-server v2 `accountSession/*` protocol used by the Desktop
profile switcher and the backend account metadata client needed to
populate workspace choices.

This is the protocol layer only. The app-server lifecycle and
consolidated saved-session storage are split into a follow-up PR.

## Rust Stack

1. This PR
2. [openai/codex#25383](https://github.com/openai/codex/pull/25383) adds
app-server session lifecycle behavior and consolidated saved-session
storage.

## Validation

- Generated app-server schema fixtures are included from the existing
generation flow in the lifecycle PR where the routes are registered.
- Did not run tests per requested scope.

codex-rs/backend-client/src/client.rs

@@ -1,3 +1,4 @@
+use crate::types::AccountsCheckResponse;
 use crate::types::CodeTaskDetailsResponse;
 use crate::types::ConfigBundleResponse;
 use crate::types::PaginatedListTaskListItem;
@@ -302,6 +303,16 @@ impl Client {
         Ok(Self::rate_limit_snapshots_from_payload(payload))
     }
 
+    pub async fn get_accounts_check(&self) -> Result<AccountsCheckResponse> {
+        let url = match self.path_style {
+            PathStyle::CodexApi => format!("{}/api/codex/accounts/check", self.base_url),
+            PathStyle::ChatGptApi => format!("{}/wham/accounts/check", self.base_url),
+        };
+        let req = self.http.get(&url).headers(self.headers());
+        let (body, ct) = self.exec_request(req, "GET", &url).await?;
+        self.decode_json(&url, &ct, &body)
+    }
+
     pub async fn send_add_credits_nudge_email(
         &self,
         credit_type: AddCreditsNudgeCreditType,