It is very possible to see a decrease of their performance next season. I don't expect much that Liverpool to go far in UCL. I just expect Liverpool can stay in the top 5 of EPL standings. With a new coach, the minimum target should be UCL zone. They surely won't try to target competing for the title in the next season.
We really have to first see how Liverpool will perform next season. This all happened because they parted ways with Jurgen Klopp, otherwise maybe they would still be considered to be able to compete in the Champions League next season.
New coaches usually bring new changes and that's something we still can't fully predict because we haven't seen how they play under the new coaching. If they play well then the opportunity is great for them, but if otherwise, then they might not be able to compete.
I also probably won't expect much from Liverpool for now, because I have to first see how they perform.
Arsenal is not a team anyone will see and believe that they can stop Real Madrid from winning the competition. Maybe if they meet in a more intense round they will try to win. In football, not everyone can be looked down on, so I won’t say Arsenal can’t do it if they try. The priority of Arsenal might be the premier league but I think they’ll also try their best in the champions league since they’re already there and won’t want to be exited from the competition with disgrace. As it stands, the best teams still remain Manchester City and Real Madrid as you said, we expect a more tougher competition, so I hope more teams will show more improvement when the competition begins.
By calculating the chances, it is true that Arsenal has a chance under Real Madrid, but as you said, this is football and anything can happen. Even though on paper Arsenal is not better than Real Madrid, it is not impossible if they can beat Real Madrid if they meet later.
They also definitely want the best and they will work hard to get the best results. No team can be underestimated even if their chances are not greater. We can see things like this happening in football. For example, the results of the semifinal match between Paris Saint Germain and Borussia Dortmund this season. Even though Paris Saint Germain is the favorite, it is Borussia Dortmund who can win.