I think everything was clear after the first game and the players of Hamburg did not believe in a positive outcome - with such a mood (objectively justified when the result of the whole season has already been lost) it is difficult to win even with a minimum score (which will not give anything anyway). Plus, by the end of the season, Stuttgart got in good shape (by the way, they took away points from Dortmund by drawing with it - as it turns out, this was way important) and therefore they easily won the second game as well.
The result from the first leg was enough to determine the second leg. As you said that stuttgart was coming stronger once bundesliga was reaching the end of season but hamburg can take it as an experience to perform even better next season.
It was sad to see Hamburg placed at the third place.. There were only 1 point gaps to some clubs above it which has been promoting to the bundesliga instantly.
I guess that if schalke will be dominating the next season. Im still having hope for schalke to stay in the bundesliga 2 only for 1 season.
It will be coming back again to the bundesliga after next season.
Stuttgart was above hamburg in any metricts. It's the reason why hamburg can be beaten easily by stuttgart. Nice try from hamburger this season. I hope it will be lucky enough next season.