The images here will help in understanding how the locks on tansu chests operate and provide a close up of interior lock components.
In the older “floriate” button locks, the button is pushed up, and locks the drawer by releasing a central steel bar with two springy legs. Keys are used to unlock by clasping these legs back together so the lock bar can fall downward, captured by another interior lock piece. Other variations exist.
Later locks have keys that both lock and unlock the mechanism.
I have sometimes wired the lock bars so they can travel freely without the legs being released when keys are lost.