I think for priority queue it will be klogk because for inserting k elements will take O(k) and for heapify process take O(logk) so I think the overall complexity is O(klogk) and for this quest is O(nmklogk).
can you correct me where i am going wrong?

The k elements aren’t inserted at every single iteration. At each iteration, you push and pop only once, so for each iteration it takes O(\log{k}) time.

but at first we insert k elements in priority queue so that time it will take klogk after that we only take care about single element then i think it will be logk.

so suppose if I insert N elemnts in priority queue then I will take NlogN so I think the for klogk case is correct.