I feel like they were working on in-engine cutscenes and then just cut them due to time constraints, the first things we saw were all from the second half of the game. It's probably hard to craft a campaign out of relatively little story to work with in comparison to the past. I suspect the season pass is mostly stuff they couldn't get finished on time. Any chance of a fullburst one on this? Might wait til then.
The story content in pack 1 and 2 are side stories on Shikamaru and Gaara. They're not anything that's from the war or the Madara fights. So far all we know on the Shikamaru stuff is that it takes place two years after the war and around when The Last happens. No info on the Gaara side story yet.
As far as a "Full Burst" goes, it's very unlikely because the only reason they did a Full Burst for Storm 3 was because they were porting Storm 3 to the PC so they figured they might as well do some new content for it and release it as an 'expansion' or new title for PC.
With three DLC packs and all the information on what they contain laid out it's pretty clear that's all we're getting.