If Stuttgart continues with its current performance in the Bundesliga, I see no club that will stop Stuttgart from qualifying for next season's UEFA Champions League. Stuttgart has been unbeaten in their last eight matches in the Bundesliga, and Stuttgart is leading Leipzig with seven points, which will make it difficult for Leipzig to finish in the top four of La Liga.
Leipzig is also in the Bundesliga not in La Liga and I think you are a little mistaken in this regard and for Stuttgart they just need to maintain their own position until the end of the season by continuing to win in every remaining game. And at least Stuttgart can be in that position in order to enter the Champions League competition next season, because Leipzig is still hindered by Dortmund in terms of fighting for the top four positions in the Bundesliga standings.
Stuttgart is 6 points ahead of Dortmund and 7 points ahead of Leipzig, of course, so Stuttgart is still quite safe in its position and also Stuttgart's recent performance is quite good so that in the remaining 8 Bundesliga matches this season, it is very possible for Stuttgart to be able to maintain its position.
Leipzig is now only competing with Dortmund and the two teams are only separated by 1 point, this will create quite fierce competition for both teams to get tickets to the UCL next season.