In order to use await, the function directly enclosing it needs to be async. According to your comment, adding async to the inner function fixes your issue, so I'll post that here:

export const sendVerificationEmail = async () =>
  async (dispatch) => {
    try {
      dispatch({ type: EMAIL_FETCHING, payload: true });
      await Auth.sendEmailVerification();
      dispatch({ type: EMAIL_FETCHING, payload: false }))
    } catch (error) {
      dispatch({ type: EMAIL_FETCHING, payload: false });
      throw new Error(error);
    }
  };

Possibly, you could remove the async from the outer function because it does not contain any asynchronous operations, but that would depend on whether the caller of that sendVerificationEmail is expecting sendVerificationEmail to return a promise or not.

Solution

Use the await directly inside the scope you are using async and remove the top scope async as it's redundant.

The correct way to write this:

const sendVerificationEmail = () =>
  async (dispatch) => {
    await Auth.sendEmailVerification();
    // some code..
  };

Elaboration

You had the error because you used the await keyword without the async directly in the scope with the await, you had 2 functions there, one inside the other, you had async on the top one but not on the inner one, where it matters.

Wrong way:

const sendVerificationEmail = async () =>
  // notice that an async before the (dispatch) is missing
  (dispatch) => {
    await Auth.sendEmailVerification();
    // some code..
  };

From this, an error will be generated (the latest error available from Chrome):

Uncaught SyntaxError: await is only valid in async functions and the top level bodies of modules

Reference

Async Functions

An async function is a function declared with the async keyword, and the await keyword is permitted within it. The async and await keywords enable asynchronous, promise-based behavior to be written in a cleaner style, avoiding the need to explicitly configure promise chains.