What's the "quantum measurement problem"? And why is it a problem? I get the wave function collapses when you measure bit. But which part of this do you want to resolve in a testable way?

It’s the question of how the wave function collapses during a measurement. What exactly constitutes a “measurement”? Does the collapse happen instantaneously? Is it a real physical phenomenon or a mathematical trick?

I thought that what constitutes a measurement is well understood; it's just the entanglement between the experiment and the observer, and the process is called decoherence - and the collapse itself is a probabilistic process as a result.

AFAIK an EoT is not required to design experiments to determine if it's a real physical phenomenon vs. a mathematical trick; people are trying to think up those experiments now (at least for hidden variable models of QM).