By posting the photo to Facebook in the first place, you are giving them near unlimited freedom to do with it as they will according to their usage policies.

That freedom can only be granted by the copyright holder, however.

It's apparently a bit of a hassle to get it removed at times though. And in most cases far to late for it to really matter: https://www.youtube.com/watch?v=L6A1Lt0kvMA

I imagine on page 57 of the user agreement you give Facebook the right to make derivative works.

They are distributing the picture so you are free to file a DMCA takedown request and they would have to take it down unless your claim is obviously invalid. Embedding extra data has nothing to do with it.

Wouldn't that depend on what they use this data for, what it is, and whether they keep it regardless of taking the file down if requested ? ( GDPR, etc. )

No.

Its metadata, I doubt it does anything.

Metadata is data.

Facebook also compresses your pictures, and I don't think anyone would seriously consider this as an infringement on your copyrighted material.

I don't use any of their services myself, nor do I suggest infringement.

I ask what is the legal situation for a copyright holder, given users likely are not aware of this data being added to a file; what the data exactly is, where or if this data is kept by them independently of the file itself, what is it used for, GDPR implications, etc.

Copyright applies to published works. Which in this case would be an image. Owning the rights to an image is a legal issue that is not concerned with representation.

So if the images is converted to digital form, then compressed then decompressed, then printed out then usually it would be considered the same image.