I really liked @tjvantoll article Handling Failed HTTP Responses With fetch(). The one thing I found annoying with it, though, is that response.statusText always returns the generic error message associated with the error code. Most APIs, however, will generally return some kind of useful, more human friendly message in the body.
Here's a modification that will capture this message. The key is that rather than throwing an error, you just throw the response and then process it in the catch block to extract the message in the body:
fetch("/api/foo")
.then( response => {
if (!response.ok) { throw response }
return response.json() //we only get here if there is no error
})