From what I can see, AF-C in movie mode needs PLM. The K-3iii manual is useless at giving that information, but if you look at the specifications of the individual lenses only the PLM ones claim to be able to continuously focus in movie mode. I don’t have any PLM lenses, so can’t say how good the AF-C is.
If video is a major use-case for you, I would suggest other options would be better.
The AF-C for normal photography is light years ahead of previous Pentax DSLRs, but still takes some practice and experimentation. I have found even the older SDM of the DA*300 can produce good results with birds in flight with lots of Z axis motion (eg puffins flying towards you). For portraits I still rely on AF-S single and focus/recompose to nail the eye focus. I have tried using face/eye detection and it works quite well, but isn’t close to 100% perfect.
The high ISO performance is a bit better than the K-1, and the stabilisation is substantially better.
The LV focus seems quick and accurate with most lenses, but I still find the Sigma 18-35 F1.8 can be hit/miss in both LV and OVF modes. The touchscreen is very responsive and allows easy focus point selection in LV.
I’ve had the K-3iii for almost a year now and it is my choice for action/walk round. K-1 still has an edge for portrait and landscape, but that is probably partly down to the lenses: DFA 15-30, DFA* 50 and FA ltd 77 are better than the equivalent lenses I have for APSC.
Hope that helps