I agree with you that Champions League will be more competitive next season. The Leverkusen team is very strong despite not having many star players. On the other hand, Manchester City will try to strengthen their squad next season. Reigning champions Real Madrid have already managed to strengthen their squad by adding Mbappe to the squad.
Just by looking out the clubs we have already gotten an insight of how next season champions League will look like and the clubs that has a very higher chance of winning and also in the case of Liverpool I would say that they should just focus on the premier League for now because with what they did on this finished season I don't think they will survive on the champions League and also they are still going to go through a little declining in performance as there coach Klopp will no longer be with them next season, so getting use to the new coach will certainly take some time and also Arsenal on the other hand should also focus on the premier League more because that's were they have the higher chance on, however in terms of real Madrid they have already equipped themselves and they are ready for the champions League.
As for me, I view the next season's Champions League as a tough one. For now, I can't fully say which team will not do well in the Champions League because the season has not yet started. Even if we should predict it, it will be best that the competition starts first.
Let’s know that there are some teams that will did well this season but will not perform well next season, and there will be teams that may experience poor performance this season but do well next season because of some factors. So, predicting that Liverpool will not perform well in next season's Champions League may be wrong. This season’s performance can’t fully judge their next season.
As for Arsenal, they can focus on all competitions and may likely do well. If Arsenal can sign some quality players to strengthen their squad, I believe Arsenal may do well in all competitions, just like Liverpool.