I don't think what you want is possible with an RGBa PNG image.  This has little to do with GIMP itself. The problem is that it's a lossless format, so it's always going to be bigger than a corresponding RGB JPEG which is a lossy format that allows you to add compression to keep the file size down. 

You might want to consider trying a different format such as WebP. GIMP can export in that format. It allows you to use lossy compression like a jpeg, but retain the alpha transparency.

An example. Here's a WebP image that is around 24kb.  I saved this at 100% quality, so compression is minimal.  The only downside is that not everything supports WebP - some image sharing sites such as imgur don't.  Some older browsers might not support it either.

Here are my WebP export settings

[![enter image description here][1]][1]

And here is the file size

[![enter image description here][2]][2]

 


  [1]: https://i.sstatic.net/3MHsP.png
  [2]: https://i.sstatic.net/lBRoE.png