Tough to know. I think it'll be a while because it would require at least a 33.2MP sensor, and oddly the industry actually has kinda reversed the MP wars to focus on other things. Some of that is also their insistence on going with smaller phones, and while you can have high MP small sensors, you end up not really making great use of the extra resolution (in some cases it can, but others it doesn't and actually might work against it). It is possible that they'll reach diminishing returns and need to start upping MP count.
There is a possibility they'll do some sort of stitching thing. They've been testing multiple sensors (for various things) for a while (one was to be able to shift focal point of pictures, which is the big use especially for "portrait" modes that they've been pushing). There was one company that had a prototype where the entire back of the phone had sensors (they were spaced out, there was like 10-30 of them I think? They varied in focal length and maybe even size, so you could actually get some quality zoom and stuff as well without having to fuss with any movable sensor parts; I think it could also compensate for shaky cam issues too). I wouldn't be surprised to see some start doing 3-4 sensors (set at different focal lengths) and stitching/blending them together, which would offer more detail and color information, without having to push right to 8K. [Not sure that focal length is the right term, but basically each sensor/lens would be focused on a different distances, one for far away, one intermediate, and then one for closer, and maybe a 4th for macro.]
I also wonder if they might find a way to stack sensors, and then be able to do different sort of filters. So to get farther away shots, it'd be one of the lower sensors (so farther from the lens), with the higher ones focused on light and color. And then you could change it up depending on what you were wanting (and say maybe for black and white pics, you could have one or two for detail and one for color). Maybe on the outermost layer they'd put an OLED that could then offer up color, polarizing, gradient, and other filters.
I almost wonder if we might not see companies separate the camera modules from the rest of the phone, enabling you to do various other things (i.e. instead of holding up a big phone/tablet, you can hold up/mount a smaller camera module, that would be able to have a bigger sensor, multiple sensors so that it can do seemless panoramas, various depth work). Think something about the size of a roll of pennies, where it could offer zoom capabilities, but ease of carry/handling. Or even a stylus, where one end would house the sensor (maybe make it so you can swap ends, so you can get different lens effects, much like how you can buy those clip-on lenses).
With AR, I'd actually say this is almost a certainty, where the glasses would have say two camera sensors, then you could link more cameras (hotlink to stuff like drones/other cameras).
Anyway, enough rampant speculation and off the wall thoughts, back to the original question. I think this is an area where standalone cameras (not talking stuff like DSLR, more like the 360/VR/panoramic ones) is probably going to differentiate themselves. Actually I think there's already one or two that does 8K already even. I want to say I've even seen one touting 16K capability.
4k hasn't hit critical mass yet so I doubt it for at least 5 years. May have a single company try the feature but it won't be anything but a novelty.
I'm not sure that has anything to do with it. The Note 3 could record 4K 4 years ago. I think there's some companies showing of 8K VR headsets, so there's definitely some companies still looking to push specs for the sake of it.