A Promise/async/await implementation of 'async.auto' is trivial, as you can use the behavior of promises themselves to avoid solving the graph:

  async function Promise_auto(tasks) {
      const keys = Object.keys(tasks);
      const results = { };
      const taskPromises = { };
      function runTask(key) {
          if (!taskPromises[key]) {
              taskPromises[key] = (async () => {
                  let fn = tasks[key];
                  if (fn instanceof Array) {
                      const deps = fn.slice(0, -1);
                      fn = fn.slice(-1)[0];
                      await Promise.all(deps.map(runTask));
                  }
                  results[key] = await fn(results);
              })();
          }
          return taskPromises[key];
      }
      await Promise.all(keys.map(runTask));
      return results;
  }

Usage example (terms intentionally out of order):

  (async () => {
      const start = new Date();
      const results = await Promise_auto({
          write_file: ['get_data', 'make_folder', async (results) => {
              console.log('in write_file', results);
              await Promise.delay(1000);
              return 'filename';
          }],
          email_link: ['write_file', async (results) => {
              console.log('in email_link', results);
              await Promise.delay(1000);
              return {file: results.write_file, email: '[email protected]'};
          }],
          get_data: async () => {
              console.log('in get_data');
              await Promise.delay(1000);
              return [ 'data', 'converted to array' ];
          },
          make_folder: async () => {
              console.log('in make_folder');
              await Promise.delay(900);
              return 'folder';
          },
      });
      console.log('results = ', results);
      console.log(`It took ${(new Date() - start) / 1000} seconds`);
  })();