So, Preserving Teamwork and Preserving in Battle weeklies have been up twice together so far this season. Normally it’s possible to complete these both at the same time, because BG Blitz grants its earned honor credit to both quests.
However, Eye of the Storm’s Blitz variant seems to not be contributing to Preserving in Battle, as not a single point of honor earned in the battle I just completed counted towards it. While yes, Preserving in Battle does state “random battlegrounds”, Blitz has been contributing to it all expansion, so it seems relatively intended that playing Blitz and having it count is a nice bonus.