So, in reading through this, I see several problems, but the authors note these mostly. The primary being that they used two different methods of detecting DNA in the vaccine samples and got two wildly different values. The qPCR returned normal numbers and their fluorometry had wildly higher numbers. It's been years since I've done a fluorometry study, but I feel like my qPCR numbers were usually more reliable. If that's still the case, saying that widely distributed vaccines have high amounts of DNA in them is just wrong, because the qPCR values returned numbers well under the FDA acceptable amount of DNA in the COVID vaccine.
And saying that they detected DNA fragments at all is something of an 'uh duh, yeah' statement for the title. You'll always find SOME DNA fragments. As long as they are under some identified acceptable boundary (hopefully itself established in other studies) then it shouldn't affect the vaccine's efficacy or increase SAEs. Add to that VAERS is there to report EVERY adverse event that happens during vaccine trials and afterward, finding a correlation between DNA found in vaccines and increased reports in VAERS is like finding a correlation between increases in butter sales in Maine correlates with increased murder rates in Chicago. It's somewhat interesting right now, but definitely doesn't rise to the level "holy shit, we need to re-science this ASAP!"