APIRunRun allows you to move or add a product to a category by simple drag & drop.
The icon located on the Products panel toolbar, is a switch that changes the behavior for dragging and dropping products from one category to another.
Following the principle of working in bulk, you can select multiple products before dragging/dropping them onto another category, to add or move them.
Note that there is another method you can use to add/move products using the Categories panel in the Properties column, where you can also remove products from categories. Please refer to the article below to find out more.