When you sync from Lightroom Desktop to Lightroom Web, the images are sync'd using Smart Previews which are 2560pixels on the long edge.
If you want the full resolution images on the Mobile device, you'll want to import them to the mobile device itself and sync to Lightroom Web from Lightroom Mobile first.
Hope this helps, let us know if you have further questions.
Using smart previews is a real limitation for the new 4K capable Apple TV and the LR app there. The images are clearly not 4K. I was able to export at max resolution from LR collections to the Apple Photos app (I did this via the camera roll on iOS. Could also do it on Mac I presume.) Then the Photos app on TVOS displays at clearly higher resolution than the LR app, presumably full 4K.
Really need higher resolution smart previews, at least optionally, for proper 4K display on the new AppleTV. This would really help on iPads also when one wants to zoom into check detail and sharpening.