I think the issue is we need to separate the 'expected'/obvious quantum effects, from the unexpected ones. For instance, some of your questions refer to quantum mechanics in molecular structure. In the most trivial sense, we couldn't even have molecular structure or even stable atoms if $\hbar \rightarrow 0$ such that there are no quantum effects. So in a trivial sense, every protein structure is due to quantum mechanics. Following up on this...

I mean, if I do not neglect electron-electron interaction, then pretty much all electrons in a condensed matter system are entangled, are they not?

Yes. In the simplest picture of matter, chemists refer to electrons occupying molecular orbitals. This is the Hartee-Fock approximation in quantum chemistry, and since the wavefunction is written as a slater determinant of the occupied molecular orbitals, in this approximation there is no electron-electron position correlation. Obviously in the real world this is not the case. The wavefunction will be correlated to have two electrons further apart on average than in the simplified molecular orbital picture. This means the state is not a product state and there is indeed entanglement of the electron positions. So you are correct on this.

(And as an aside, more advanced multi-electron computational methods beyond Hartree-Fock can of course be used to account for most of this correlation energy in theoretical calculations. The molecular orbit picture works very well though, which is why this is how it is introduced to students and how chemists colloquially discuss and visualize the quantum mechanics of a molecule.)

However, again this is in some sense the 'trivial' effects of quantum mechanics. But as we get to larger structures, due to interaction with the environment and decoherence, we can increasingly well describe everything with phenomenological parameters and a classical theory. True the phenomenological parameters are due to the quantum mechanics, but this is not the exciting part.

The exciting part is when we can't describe the protein interactions with phenomenological models due to the quantum coherence playing an important part at the macroscopic level.

Yes, it is somewhat arbitrary where we draw this line. But few really thought biology would end up using something so fragile as the coherence of entangled states to actually improve biological function. The better studied example I've seen regarding this is energy transfer in a particular photosynthesis step.

Whether something is amazing or not isn't really a scientific question, but hopefully I clarified enough regarding your question of entanglement of electrons in molecules to see how the use of coherence to improve biological function is at the least unexpected, and hopefully exciting to you as well.

I think the issue is we need to separate the 'expected'/obvious quantum effects, from the unexpected ones. For instance, some of your questions refer to quantum mechanics in molecular structure. In the most trivial sense, we couldn't even have molecular structure or even stable atoms if $\hbar \rightarrow 0$ such that there are no quantum effects. So in a trivial sense, every protein structure is due to quantum mechanics. Following up on this...

I mean, if I do not neglect electron-electron interaction, then pretty much all electrons in a condensed matter system are entangled, are they not?

Yes. In the simplest picture of matter, chemists refer to electrons occupying molecular orbitals. This is the Hartee-Fock approximation in quantum chemistry, and since the wavefunction is written as a slater determinant of the occupied molecular orbitals, in this approximation there is no electron-electron position correlation. Obviously in the real world this is not the case. The wavefunction will be correlated to have two electrons further apart on average than in the simplified molecular orbital picture. This means the state is not a product state and there is indeed entanglement of the electron positions. So you are correct on this.

(And as an aside, more advanced multi-electron computational methods beyond Hartree-Fock can of course be used to account for most of this correlation energy in theoretical calculations. The molecular orbit picture works very well though, which is why this is how it is introduced to students and how chemists colloquially discuss and visualize the quantum mechanics of a molecule.)

However, again this is in some sense the 'trivial' effects of quantum mechanics, as it is just "chemistry". But as we get to larger structures, due to interaction with the environment and decoherence, we can increasingly well describe everything with phenomenological parameters and a classical theory. True the phenomenological parameters are due to the quantum mechanics, but this is not the exciting part.

The exciting part is when we can't describe the protein interactions with phenomenological models due to the quantum coherence playing an important part at the macroscopic level.

Yes, it is somewhat arbitrary where we draw this line. But few really thought biology would end up using something so fragile as the coherence of entangled states to actually improve biological function. The better studied example I've seen regarding this is energy transfer in a particular photosynthesis step.

Whether something is amazing or not isn't really a scientific question, but hopefully I clarified enough regarding your question of entanglement of electrons in molecules to see how the use of coherence to improve biological function is at the least unexpected, and hopefully exciting to you as well.