It's quite challenging to keep the text legible within a 1KB limit. Here I manually removed a few details that more-or-less weren't visible post-compression anyway, then cut the color palette a little. You have to use such a low resolution with such high compression that almost everything gets amputated to keep the text kinda-readable (and even AVIF and JPEG XL (which are usually better than WebP) struggled, at least in my editor): https://files.catbox.moe/eyp2w7.webp

If you can live with 2KB, you don't have to amputate nearly as much: https://files.catbox.moe/g5htfo.webp

In both cases I manually reconstructed the top of the star, but that's a bit "extra" lol.

And just for comparison, no text and 10KB at "full" res: https://files.catbox.moe/9bkn21.webp

The same thing but half res (more optimal at this file size): https://files.catbox.moe/cac65u.webp

Valmond's implicit suggestion of not just quantizing as a pre-processing step (which is what I foolishly did), but actually reducing the saved bit depth of the image might give you something that looks much better overall than what any of the WebP versions we've been playing with here do - if you put in more effort!

Here's an example of a not-fully-optimized implementation that gets down to ~2.5KB as a PNG, or ~2KB as a lossless WebP (i.e., the two images are identical in quality):

• https://files.catbox.moe/pjedam.png
• https://files.catbox.moe/ua0qnh.webp

With some judicious manual optimization (which I haven't done here), it's plausible you could get this down to 1KB with better overall fidelity than the lossy WebP versions we've been playing with. Not 100% sure, as optimizing images for file sizes this small is not really my wheelhouse!

My main concern with this approach is that you're bottlenecked by resolution - large areas of plain color have a hard limit on their compression with PNG, but lossy compression can go wild with stuff like that.