Leverkusen will play in the Champions League, but they will probably be thrown into the Europa League if they fail in the group stages.
I would like to fix a misinformation here. There isn't such thing like dropping from one European tournament to another anymore. Therefore the thing you say is impossible to happen.

People are already discussing whether this is a good decision or not. Because you know there are mostly better teams competing in the Champions League. Teams coming from there after the group stage were making the Europa League more interesting and increasing the quality of it as well. But from now on I'm curious about how things will go. There is no more group stage format either, instead there is a format similar to league but not exactly the same.
If we look at the format of the Champions League this season, of course every team which fails to qualify from the group phase and is in third place in the Champions League group, of course they will automatically play in the European League, but next season the Champions League has used a new format in their competition, so we cannot be sure that every team that fails in the Champions League next season will play in Europe or not at all, but seeing Leverkusen impressive performance this season, of course maybe they will be able to create surprises again later, but regardless of that, of course Alonso must be able to maintain their squad this season to compete in the tight Champions League next season.
The European League next season has officially also used a new format in their competition, so it is likely that there will be many changes that will occur so that we can see a tighter competition later, so far there are several big teams that have confirmed that they will play in the European league, so of course the European league may be fierce like the Champions League later in a new format.