Does the new finding on "reversing a quantum jump mid-flight" rule out any interpretations of QM?
No. All news stories about this result are extremely misleading.
The "quantum jump" paper demonstrates an interesting and novel experimental technique. However, it says absolutely nothing about the interpretation of quantum mechanics. It agrees with all proper interpretations, including the Copenhagen interpretation.
What the researchers actually did
When a quantum system transitions between two states, say $|0 \rangle$ to $|1 \rangle$, the full time-dependence of the quantum state looks like $$|\psi(t) \rangle = c_0(t) |0 \rangle + c_1(t) |1 \rangle.$$ The amplitude $c_0(t)$ to be in $|0 \rangle$ smoothly and gradually decreases, while the amplitude $c_1(t)$ to be in $|1 \rangle$ smoothly and gradually increases. You can read this off right from the Schrodinger equation, and it has been known for a hundred years. It is completely standard textbook material. The researches essentially observed this amplitude changing in the middle of a transition, in a context where nobody had done so before.
The authors themselves emphasize in their paper that what they found is in complete agreement with standard quantum mechanics. Yet countless news articles are describing the paper as a refutation of "quantum jumps", which proves the Copenhagen interpretation wrong and Bohmian mechanics right. Absolutely nothing about this is true.
Why all news articles got it wrong
The core problem is that popsci starts from a notion of "quantum jumps", which itself is wrong. As the popular articles and books would have it, quantum mechanics is just like classical mechanics, but particles can mysteriously, randomly, and instantly teleport around. Quantum mechanics says no such thing. This story is just a crutch to help explain how quantum particles can behave differently from classical ones, and a rather poor one at that. (I try to give some better intuition here.) No physicist actually believes that quantum jumps in this sense are a thing. The experiment indeed shows this picture is wrong, but so do thousands of existing experiments.
The reason that even good popsci outlets used this crutch is two-fold. First off, the founders of quantum mechanics really did have a notion of quantum jumps. However, they were talking about something different: the fact that there is no quantum state "in between" $|0 \rangle$ and $|1 \rangle$ (which, e.g. could be atomic energy levels) such as $|1/2 \rangle$. The interpolating states are just superpositions of $|0 \rangle$ and $|1 \rangle$. This is standard textbook material: the states are discrete, but the time evolution is continuous because the coefficients $c_0(t)/c_1(t)$ can vary continuously. But the distinction is rarely made in popsci.
(To be fair, there was an incredibly short period in the tumultuous beginning of "old quantum theory" where some people did think of quantum transitions as discontinuous. However, that view has been irrelevant for a century. Not every early quote from the founders of QM should be taken seriously; we know better now.)
Second off, the original press release from the research group had the same language about quantum jumps. Now, I understand what they were trying to do. They wanted to give their paper, about a rather technical aspect of experimental measurement, a compelling narrative. And they didn't say anything technically wrong in their press release. But they should've known that their framing was basically begging to be misinterpreted to make their work look more revolutionary than it actually is.
Interpretations of quantum mechanics
There's a very naive interpretation of quantum mechanics, which I'll call "dumb Copenhagen". In dumb Copenhagen, everything evolves nicely by the Schrodinger equation, but when any atomic-scale system interacts with any larger system, its state instantly "collapses". This experiment indeed contradicts dumb Copenhagen, but it's far from the first to; physicists have known that dumb Copenhagen doesn't work for 50 years. (To be fair, it is used as a crutch in introductory textbooks to avoid having to say too much about the measurement process.) We know the process of measurement is intimately tied to decoherence, which is perfectly continuous. Copenhagen and, say, many worlds just differ on how to treat branches of a superposition that have completely decohered.
Another issue is that proponents of Bohmian mechanics seem to latch onto every new experimental result and call it a proof that their interpretation alone is right, even when it's perfectly compatible with standard QM. To physicists, Bohmian mechanics is a series of ugly and complicated hacks, about ten times as bad as the ether, which is why it took last place in a poll of researchers working in quantum foundations. But many others really like it. For instance, philosophers who prefer realist interpretations of quantum mechanics love it because it lets them say that quantum mechanics is "really" classical mechanics underneath (which actually isn't true even in Bohmian mechanics), and hence avoid grappling with the implications of QM proper. (I rant about this a little more here.)
Quantum mechanics is one of the most robust and successful frameworks we have ever devised. If you hear any news article saying that something fundamental about our understanding of it has changed, there is a 99.9% chance it's wrong. Don't believe everything you read!