Q.My ligustrum has empty branches- with very tiny tiny leaves
Started out with just empty branches.. I thought dead, but when broken off showed still green. Watered ALOT.
Still look sickly but branches covered with tiny tiny leaves

Certified GKH Gardening Expert
It sounds like winter injury. My Sunshine ligustrum had bare branches. Is that what yours is or is it Golden? The fact your leaves started to come back is a good sign. Go ahead and prune out the dead wood. Give it a light application of general fertilizer if you haven't already. Water if rain is not sufficient.
https://www.gardeningknowhow.com/plant-problems/environmental/winter-burn-in-evergreens.htm
https://www.gardeningknowhow.com/ornamental/shrubs/shgen/winter-damage-of-shrubs.htm