always turn to face the camera
A billboard is a flat quad that is rotated every frame to face the camera. Health bars, damage numbers, name tags and distant trees are billboards, so they read the same from any angle. In the demo, the left health bar is fixed to its character and turns edge on or mirrored, while the right one stays readable.
Make the health bars and name tags billboards: each frame, set each quad's world rotation to the camera's rotation so it faces the screen, and for trees and other upright sprites rotate only around the Y axis so they stay vertical.