Try to setOption useWorker: false

      <AceEditor
        mode="json"
        theme="github"
        onChange={onChange}
        name="UNIQUE_ID_OF_DIV"
        editorProps={{ $blockScrolling: true }}
        setOptions={{
          useWorker: false
        }}
      />

This doesn't work, because editSession uses web worker to generate annotations which is async:

editSession.on('changeAnnotation', () => {
    let annotations = editSession.getAnnotations();
    callback(null, annotations)
});

docs

Note that currently each editSession creates a new worker, so it is better to use setValue on an existing instance of editSession, or call editSession.destroy() before calling the callback

So a full solution might look like:

const getAnnotationsPromise = (value, mode)=> {
  const editSession = new EditSession(value);
  editSession.setMode(`ace/mode/${mode}`);

  return new Promise((resolve)=> {
    editSession.on('changeAnnotation', () => {
      const annotations = editSession.getAnnotations();
      editSession.removeAllListeners('changeAnnotation');
      editSession.destroy();
      resolve(annotations);
    });
  });
};