I split this into two requests as they will likely be implemented separately. Here's a link to the one for drag-and-drop so you can Follow it (I've added your vote already): https://feedback.telerik.com/blazor/1427751.
At the time of writing, selection is available only in the grid, so you can see if that will fit your needs: docs and demo.
Alternatively, you can also implement templates for the treeview item to handle click events with your own code and alter the model to denote selection. The field in the model that will denote selection can also be used to add a class to showcase selection.