Most people don't know your photos can be cross profiled and identified by the unique noise signature of your camera.

I've never heard of it being used in practice though. There's a github repo somewhere if you're interested in trying it yourself.

If I’m sharing images, I’m generally sharing links to images, or images I’ve created myself and scrubbed of metadata, plus touched up, usually with a noise mask, among other things.

Wouldn't recoding or using other compression methods break that?

It's something to be aware of if you are trying to record/send images in secret. But it's not a problem if you are passing on an image you found somewhere else. You leave no trace if you are just passing the image, so the image itself is of no concern privacy-wise.

It sure is possible to embed invisible information into videos and images, it's called metadata. Now you might think of other techniques, e.g. https://en.wikipedia.org/wiki/Steganography but most if not all are, AFAIK (and I won't pretend I know the state of the art in the domain) if they are within the data itself (thus become data, not meta-data), e.g. a visible stamp in an image, are made to remain visible. Compression codecs are specifically targeting the visible or audible spectrum. One of the most basic way to "compress" lossy information (as opposed to lossless) is precisely to remove the ends of the spectrum that is not perceived by the average human audience.

So... AFAICT it's either visible and thus can be spotted (and thus can be removed, even if by adding a black mark over) or not visible but then most likely will be removed by basic compression codecs even without trying to do so.

TL;DR: no and I wouldn't be until I see this in the wild (not a research paper claimed it's technically possible).

I didn't think of this. Can they embed dynamic info that logs ip and identifying info?

It's definitely possible. I've heard the film industry does do this with theatrical releases so they can determine what theater a copy came from (and determine the seat it was recorded from by the angle). I don't really share images/video anonymously though, so don't think about it much. When I rarely do, I try to check for and strip metadata.