I agree with you that Manchester City's overall performance has improved somewhat. Manchester City have won their last two Premier League matches against Leicester City and West Ham. City won 4-1 against West Ham. However, these two opponents of Manchester City were not that strong. Manchester City won against weak opponents. I doubt whether City can play well against a strong team like PSG.
PSG is a very strong team under Luis Enrique. There are several weaknesses in PSG's squad. However, PSG's overall performance is very strong. I believe PSG will not lose this match, it is PSG's home match. PSG will win this match or the match will be drawn. I do not expect Manchester City to win this match. City's overall performance is still inconsistent.
The match against PSG is very important for Manchester City because if they lose, of course their position in the standings will get worse. Their improvement in the Premier League has been very good but in the Champions League they really have to try to perform better because the opponents they face are the strongest team in Ligue 1. PSG is also the same as Manchester City where they did not perform well in the Champions League so choosing a winner in this match is very difficult.
Halaand is the hope of City fans to be able to beat PSG, his goal contribution is very much expected in this difficult match. Pep Guardiola will certainly field his best players in this match, they have to work better from the first minute and be able to stabilize their playing style throughout the 90 minutes. My assumption, that if one of the teams manages to score an early goal then they can be the winner.