Currently, the only way to rearrange items is to sort them by ID or by Name (Help Documentation: Manage styles). If users want to arrange their styles in a specific way, current guidance is to "consider creating a new style and copying relevant style items to it in the desired order."
The symbology my team uses is updated rather frequently to suit the needs of our clients and field teams, and removing and adding symbol types in order to get them in the arrangement that makes the most sense for our needs is a bit cumbersome. Our symbology names don't lend themselves to being placed alphabetically, and as we add new symbols the newest ones will always be at the beginning or end (depending on the Sort), when often they need to be somewhere in the middle.
Being able to drag-and-drop to rearrange items in the style would be a small but meaningful quality of life upgrade!
