[Typescript] Annotating the Errors Thrown by a Function

/**
 * How do we annotate the errors this function throws?
 */

type PossibleErrors = SyntaxError | DOMException;

const getUserFromLocalStorage = (id: string) => {
  const user = localStorage.getItem(id);
  if (!user) {
    return undefined;
  }

  return JSON.parse(user);
};

try {
  const user = getUserFromLocalStorage("user-1");
} catch (
  // How do we make this typed as PossibleErrors?
  e
) {}

The only possible way is returning a result object from the function:

const getUserFromLocalStorage = (
  id: string,
):
  | {
      success: true;
      data: any;
    }
  | {
      success: false;
      error: SyntaxError | DOMException;
    } => {
  try {
    const user = localStorage.getItem(id);
    if (!user) {
      return {
        success: true,
        data: undefined,
      };
    }

    return {
      success: true,
      data: JSON.parse(user),
    };
  } catch (e) {
    if (e instanceof DOMException) {
      return {
        success: false,
        error: e,
      };
    }
    if (e instanceof SyntaxError) {
      return {
        success: false,
        error: e,
      };
    }
    throw e;
  }
};

const user = getUserFromLocalStorage("user-1");

if (user.success) {
  user.data;
} else {
  user.error;
}