Custom Category order in a Categories Field
No, it’s not possible to change the order of related categories.

(Think of the field as a big checkbox list; you can change which checkboxes are checked, but you can’t change their order. The only reason it’s not a simple checkbox list is to save visual space.)

If you really want to be able to set the order, you can put the Categories field inside a Matrix field, where each block selects a single category, and then you can reorder the blocks.