How is Poppy and Shyvana related?

They live in Demacia.

are they listed as friends? both are demacian soldiers of sorts after all

J4 fangirls

Your trying to look for a lore connection/relation right?

If so then you should be aware that not every champ and that's including most from Demacia, have had their lore renewed yet. So i'm not surprised you can't find a relation between the two. Plus not ever champ relation is written into their stories either, some champs just have very loose connections i.e. Warwick & Vayne. Neither of there bio's have any interaction or give any hint to them ever meeting once.

So I think the other responses are right, their only obvious connection/relation is that they're both allied to Demacia.