This image looks pretty in Gimp’s native XCF format:
After exporting to any internet format without compression it looks like this:
What’s the reason for this loss of quality, and how can I avoid it?
Any format, really? WebP? JPG?
For GIF and color-indexed PNG (is the image color-indexed?), the opacity is "binary" (fully transparent or fully opaque), so edge pixels cannot assume the partial opacity that makes things look smooth.
Otherwise, please upload the PNG to a place where it won't be altered before we can download it.