Modern phones take long exposures and try to make sense of it by analyzing it.

Basically, a one second really dark video can be summed up into one very blurry but bright enough photo. But if you carefully move each frame to compensate for camera movement when summing it up - you might also get a sharp picture. But then the subject moves, or a leaf moves, and the algorithm has to decide which parts of the photo should be a priority for not being blurry. And that would be faces, usually. So the camera now needs to decide what is a face and what isn’t. Just to take one single telephoto picture.

Only doing “in camera processing” like a 2015 digital camera with some sharpening, color curves etc doesn’t cut it anymore. If your phone does that, it’ll be laughed at. Phones these days need to do clever long exposure stacking with image recognition and all.

Wouldn't they even move different parts of the scene differently for summing up? And the summing is for denoising, not for rising levels out of darkness, so it would be perfectly fine to sum only the parts where there is plenty of confidence about the movement, leaving others noisy (or, if more noisy than one would like to admit, de-noise spatially instead of temporally in those places, which brings us back to blurry. Add an "unsharp mask" step to compensate and you get that watercolors look we all know).

Back to moving different parts differently: this seems very similar to the motion prediction parts of video encoding. I wonder if and how much the stacking algorithms make direct use of elements of the video encoding implementations those cameras also have?

Does anything like that exist as a computer-attachable cam, e.g. for Linux? Or are we stuck with <2015 cameras unless they come as part of a smartphone?

There is software to do that, yes. Many cameras are able to do smart multiframe stacking, even fairly old ones.

It's just that photographers would rather not have to rely on this, because it has a lot of issues.