You'd describe it as a tagged union in some languages. So when you say you'd return an error with extra information, what that information is is associated with the specific variant of the enum.

Using yuriks AllocError as an example, if the error is SizeTooLarge, it has the size field. Other errors may have no additional data, others may have different data.

When you return an error from your allocating function, it's a known size, the size of the largest enum variant + the discriminant (tag).

  enum AllocError {
    SizeTooLarge { size: usize },
    // etc.
  }

  enum MyApiBindingCrateError {
    // You didn't provide an 
    // API key. Maybe we should 
    // design our interface to
    // make this impossible 
    ApiKeyMissing,

    // Client was unauthorized 
    // to make this request 
    AuthorizationError,

    // The entity you requested 
    // did not exist (404'd)
    NotFoundError,

    // You're sending too many 
    // requests to the server 
    TooManyRequests,

    // That specific error with
    // the API
    // Maybe users can't delete 
    // folders until they're empty 
    // Whatever 
    SpecificApiIssue1,

    // Some other specific error
    // with the API
    SpecificApiError2,
  
    // Server didn't respond the
    // way we expected. 
    // Here's what it told us
    UnexpectedHttpResponse { 
      // HTTP status code
      status_code: StatusCode, 

      // If it had a 
      // string-encoded body
      body: Option<String>,
    },

    // Unhandled Issue with IO 
    IoError(io::Error),
  
    // Unhandled Issue with 
    // request library
    ReqwestError(reqwest::Error),

  }

Your application can be a little less structured if you want. Though with LLMs, I'm using anyhow and thiserror a lot less.