Yeah, that's not very good implementation. PetaPixel usually have good content, but using a GIF to compare these two images? Come on! You can see the compression artifacts very easily.

How about this one, by a user from here?

https://blog.wolfd.me/hubble-jwst/

This is a great way to show all the new distant details. Amazing to think that so many of the artifacts in Hubble's total darkness are galaxies upon galaxies.

Umm.. not compression artifacts. GIF uses lossless LZW. Maybe color palette artifacts since GIFs are usually palettized and not true color (although with a tortured use of local color tables they can even be true color)

This is the nitpick we all come here for :)

Choosing a limited palette in order to save bytes, some might say is compression. If said compression hurts the image quality, some might call that "compression artifacts".

The point stands, GIF was a poor choice for the format here.

This was also recently posted on reddit: https://johnedchristensen.github.io/WebbCompare/

Was J J Abrahams involved in Webb, because it really seems to produce nice lens flair

What you're seeing is not lens flares but diffraction spikes. https://en.wikipedia.org/wiki/Diffraction_spike

You could call those lens flares I guess, but commonly known as diffraction spikes when it comes to telescopes. In this case they appear because of the supporting struts in the James Webb telescope.