in that PBS video they talk about the images from the JWST and then they interview the artist "who brings them into the visible spectrum" I was surprised by how much of it was left up to artistic interpretation. its very possible the images we see from the JWST aka the ones the public sees aren't what those areas look like at all - if we hypothetically were on a rocket ship closer to them and able to look out the window.
I find this to be the most troubling, because the artistic interpretation really should be more science based imo, but that PBS video showed a guy really just making it look anyway he wanted, and he even showed different versions and just picked which one was most beautiful to look at.
I don't know, I didn't realize this was how it was done and it kind of bums me out.
First of all, you can get a decent telescope and see the thing for yourself. They will be tiny and in monochrome (not bright enough to stimulate your color vision) and you'll need a dark sky site to make the most out of them, but they're visible in my light-polluted SoCal backyard on clearer nights.
The Hubble color palette is also false color so anything you see in the Hubble images is also color-shifted to make prettier pictures. They're not shifted as far in the spectrum as the Hubble works mostly in visible wavelengths, but the emission spectra they are detecting does not line up perfectly with your eyes' R G B. The Hubble color palette maps to those wavelengths for the best visibility in public pictures.
And as others mentioned, the JWST is an infrared telescope specifically because the IR spectrum penetrates dust better than visible and probably also because IR is absorbed by our atmosphere more than visible light so the best place for an IR scope is in space, above that water vapor. Since IR is invisible to your eyes, these pictures need to be color-shifted. Otherwise you'd be looking at a pretty much blank picture of visible light.
So, yes it's completely arbitrary how they want to map the JWST's colors to visible wavelengths as it's all false color, no color is "more false" than any other color.
None of this should bum you out, it's necessary. Instead find a local dark sky site in the summer where local amateur astronomers gather on new moon weekends and ask to look through the bigger scopes there at the Eagle Nebula (where the POC are) and gather all those photons with
your own eyes. It's pretty awesome. And they love to share their views of the night skies.