Function run_account_loading 

pub async fn run_account_loading(
    account_key: AccountKey,
    workspace_weak: Weak<Workspace>,
)

Probe the account once and settle its terminal LoadingState.

Takes Weak<Workspace> so the task auto-exits when the workspace is dropped during shutdown - same pattern start_usage_poller uses. The lock is only acquired for single mutator calls, never across an await, so other workspace operations aren’t blocked.