Question batch processing

is it possible to bulk reassign topics from the search result to another category, like in the category overview?

Unfortunately, the search results can only be moved individually. The batch function can be used in the selected category, but only topics that are on the displayed page can be selected.
I don't know how big your forum is and how many topics are displayed per page. But maybe it will help you if you temporarily display e.g. 100 topics per page and search for and mark all topics that should be moved.
If you know the topic titles from the Kunena search, you can use the browser search (Ctrl + F) to quickly find and mark these titles from the 100 topics displayed.

there are about 10 thousand topics (migrated from mchelpdesk by our own program). The customer would like to categorize it into more categories and he finds it best from search. Do you have any idea where I could program this?

Or make my own view?

Unfortunately, I don't know a solution to this problem. But I don't quite understand this problem. When someone searches for a topic using the Kunena search, the topics that match the search term are displayed. This can never include all searched topics. So in my opinion, a batch function would not bring the desired relief (but I could be wrong).

it's a bit different, someone searches for topics on their terms and needs to move them all into a certain category

And you can't run a query (or multiple queries) on topics table in phpmyadmin?

I can, but the customer wants to do it himself.
So the only option is to make your own view kunena.

Or as a suggestion to incorporate into the core kunena?