I noticed an article where the author seemed to imply the halting problem was solved so I found the paper he was referencing but it is over my level of knowledge.
Was hoping someone in the community would be so kind to make a brief comment. The first link below is the article in quanta magazine and the second link is the article that is under discussion.
No, it doesn't.
What it does do is reduce the halting problem to a different type of problem, which on the face of it doesn't seem particularly related. But this doesn't mean that the halting problem is solvable, only that it's solvable relative to a different problem (which consequently is itself unsolvable).
There is in fact a rich structure of "degrees of unsolvability," more commonly called the Turing degrees. It's worth noting that in contrast with complexity theory where many-one reductions are standard, the default notion of reducibility in the context of computability theory is Turing reducibility. To see the difference, note e.g. that we trivially have a polynomial-time Turing equivalence between $\mathsf{NP}$ and $\mathsf{coNP}$ while it's open whether they are polynomial-time many-one equivalent.