Arsenal are very good at throwing away their Premier League title chance every time they have a chance these days. You would remember what happened in the recent years while they were 1 vs 1 with Manchester City.
I'm sad for them. Arteta has built a really solid team in time. There are very capable young players in the squad. Honestly I see the thing they lack for a trophy here as a reliable CF. They don't have it for a long time. Gabriel Jesus recovered from a lasting injury first and made a really good comeback too. But in a very short time, he got another serious injury and he isn't expected to return before August... Arteta is also aware of this problem but they still haven't signed anyone. If they want the title then they have no choice other than doing this.
If we talk about priority scale, both Champions League and domestic league matches are equally important.
They are currently in a difficult situation. However, even so, their position is slightly advantageous, with the goal difference they have +2, to be able to qualify for the next round in the Champions League, they do not need to wait for the results of the Befica, PSG, Sporting, and VfB matches. By successfully getting 3 points from Club Brugge, City automatically enters the top 24 because even though they will have the same points, namely 11 points with Club Brugge, Man City will be superior to Club Brugge in goal difference, because currently Club Brugge's goal difference is -2.
However, on the other hand, it is very important for Man City to be able to maintain their position in the 4th premier league standings. It is very important because this is to anticipate if they fail in the champions league this season, they still have a chance for next season. Therefore, they must give their best in every match in the premier league.