Hi friends. Before I bought the A6500, I read great praise for 4K video quality. But I'm dissatisfied. 4K video is not smooth, especially when moving with the camera from side to side. Surprisingly HD video is very nice, smooth and sharp, Im very happy with 1080P video. I use the camera with the lens ZEISS 16 - 70 F4 OSS. Is it possible that this lens is not suitable for 4K shooting? Maybe the Sony E PZ 18-105mm F4 G OSS is a better choice. But on the Internet I found some 4K videos shot with the ZEISS lens and they were all fluent. Do you have a similar experience and advice to solve the problem? Can you advise me how to set the camera for 4K shooting? I tried to change some settings like shutter speed (but I know that twice the speed of the frame rate is ideal), deactivating image stabilization, etc.
I shoot in PAL mode, 4K, 25FPS, SS 1/50, ISO AUTO, WB AUTO.

Original files (very short clips) can be downloaded here:
FHD Video (PAL, 50P, SS 1/100, ISO AUTO, WB AUTO, PP OFF): https://www.dropbox.com/s/wcf1pntnvkgtfdp/FHD.MP4?dl=0
4K Video (PAL, 25P, SS 1/50, ISO AUTO, WB AUTO, PP 4): https://www.dropbox.com/s/cg8z3q5f1k5hxih/4K.MP4?dl=0

Thank you for your help.

What SD card do you have ?

I use the recommended card. UHS1, U3. Kingtom. 90W, 90R. This is not the cause of the problem.

Exactly the same problem I have, if I shoot HD 25P. Smooth motion is only in 50P or higher. But 4K is possible just to 25P (PAL).... Any advice?