Ok, I will try. I have to admit I do not fully understand what you are asking.
As noted in the link at the top, it is reasonable to speculate that these filaments are related to the activity of the galactic centre supermassive black hole. However, we do not have a quasar in our galaxy, and it is hard to imagine (consistent with evidence from this and similar galaxies at various cosmological redshifts) that the Milky Way possessed an active galactic centre which subsequently was quenched. Indeed, part of the mystery here is that there is a quite weak magnetic field permeating the galactic centre, and little outward cosmic ray pressure.
The spectral index (more details at https://arxiv.org/abs/2201.10552 §3.1, "nonthermal radio filaments that have broad spectral index distribution as well as the steepest spectral index that can readily be discerned at high latitudes", cf https://en.wikipedia.org/wiki/Spectral_index although neither link is especially friendly to non-experts) is entirely consistent with synchrotron radiation, which does not require any exotic particles at the filamentary sources of the radio emissions. As discussed in §3.2 of the arxiv preprint, all we need is highly accelerated electrons. The mechanism for accelerating the electrons is unknown, but there are several explanations available that do not require exotic particles. §4.3 discusses several plausible alternatives.
I'm no expert on anyons but I do know how Wilczek described them when he first proposed them, and Keilmann's observations of his humour, and I struggle to see what problems introducing anyons might reasonably solve at these bulk scales. Additionally, I do not see how anyonic behaviour -- rather than straightforward magnetobremsstrahlung -- could be relevant, much less a better description, at the warm temperatures in the environments of these filaments and galactic centre molecular clouds.
Unfortunately, I don't understand your second last paragraph at all.