I've recently purchased and installed the digital deluxe edition... how do I obtain the promised bonus items, specifically, the NX prefix and the automated phaser battery?

NX might be granted normally so check the rename ship section or whatever it is called. All monetary purchases and a few free ingame items are unlocked through the special unlocks of the C-Store.

Could you be more specific? None of the promised items appear in the store on this site. Is there someplace in game I need to go?

All ingame items purchased through monetary purchase have to be claimed ingame. There is a triangle on the minimap that opens up a menu that has R&D progress, C-Store, Visit Bridge, and a few others. Need to visit the C-Store from there. NX can be selected by pressing k and going to your current ship.