Yup, the nice thing of many-worlders is that it is quite straight-forward and it is totally based on Schrodinger's equation. While in other interpretations (including Copenhagen) when the wave collapses, you have to dismiss the other states of Schrodinger's equation, in many-world interpretation you always keep the entire equation. Interestingly, the many-world interpretation seems to be quite similar to the concept of landscape in string theory. Leonard Susskind says that they are actually the same in his 'The Cosmic Landscape' book.many-worlders argue their case very well and give pretty straight-forward answers to most of the questions.
Regardless, the frame-work of quantum mechanics is ~100 years old. They added stuff and flushed it out, but its still rests on the same ideas. There are many things, that aren't figured out but there hasn't been a single observation in quantum mechanics, that wasn't predicted by the Schrödinger equation. In popular science QM ts often depicted as is this mystical idea, that nobody understands. All the (genuinely) amazing stuff, that is reported in slightly clickbaity articles, is always in agreement with the Schrödinger equation and the general frame-work. I would take any reasonable bet, that any observation/discovery in the next 40 years is also going to agree with this frame-work. It was well enough understood in the 60ies to predict what happens when we fire protons with incredible speed/energy at each other and it panned out exactly as expected, when the LHC detected the Higgs. Quantum mechanics nowadays is much more refined and advanced than it was back in the days. Just because its genuinely weird, doesn't mean that its not understood; there is always going to be a frontier towards smaller/higher-energy, because knowledge doesn't have any sensible limit.
Quantum effects could play a role when it comes to consciousness (just like they might play a role in photosynthesis), but it could also be entirely classical. Considering that we know very little about it at all, its hard to make any argument to begin with. One way or another, I don't think it changes all that much. It is certainly doesn't have anything to do with observers.
I don't think it is that nobody understands quantum mechanics, but that it is extremely hard to understand it on an intuitive level, and have good interpretations for it (this is what the likes of Bohr and Feynman meant by it). It is actually one of the most exact theories right there, and awesome at predicting and measuring things (every prediction made by quantum mechanics that eventually was put to an experiment, ended in the exact same way as the theoretical predictions), and is actually useful in technology (the concept of tunneling is massively used). The question is if quantum mechanics is all that is there and it describes the world (in which case, general relativity is wrong, but quantum mechanics is hopeless at explaining the gravity), or it is just a theory that is useful to measure things, but it is not the real cause (aka, there are hidden variables which we do not observe, and quantum mechanics is an approximation for them). I don't think that anyone really knows it and who knows if we will ever know it.
Finally, has anything fundamentally novel (in quantum mechanics) has happened since the standard model and the unification of the weak force with the electromagnetism? I am not talking about experiments that confirmed predictions (Higgs boson) or observing gravitational waves. More like, theoretically speaking, I don't know if there are massive blocks that have been added to it, I think everything is still based on Schrodinger's equation.
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