Are you looking for more information on your mare’s stamm or stallion advice?
I don’t know a lot about the particular stamms you mentioned and I haven’t personally focused heavily on female family research in my breeding decisions, but just in general my understanding is that the main signficance of tracing female families is the transmission of mitochondrial DNA (mtDNA) and haplotypes. mtDNA is inherited maternally without recombination. Stallions pass mtDNA but it is not expressed in the next generation, so your mare’s stamm is what is relevant here, not her sire’s.
I don’t think there has been nearly as much research done on sport horses as there has been on race horses, but there was an interesting study recently with Holsteiners: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8944467/
With regards to making breeding decisions, I would look at your mare’s female line and see what it has produced in sport and ideally you would like to see a female family that has consistently produced horses doing well at the upper levels of the sport (although I think that significance is often overstated and I think can result in missing out on some very good mares). However, for addressing things like jumping technique and conformation, I’d be looking at her immediate pedigree and picking a stallion that complements her by looking at him, his pedigree and what it has produced, and what he has produced himself and I wouldn’t worry as much about her stamm alone for those particular things. My (admittedly limited) understanding is that while mtDNA might be significant for jumping potential in the context of endurance, explosivity/musclar power, etc it wouldn’t be likely to have nearly as much significance in terms of conformation or leg technique over the jump. I’d do a bit of research on which crosses worked well, looking through the horses in your mare’s pedigree and their other offspring, and then focus on choosing a stallion that consistently added size, suited a longer backed mare, and had good jumping technique himself. Untouchable and Colorit come to mind as Holsteiner approved option, depending on the rest of your mare’s pedigree and whether frozen is an option.