Although only their last two games have looked promising but honestly I will not fully believe that Chelsea will really change for the better, but on the other hand yes maybe the success in the last two games is enough to indicate that there are signs of change from Pochettino's squad, although I will first fully believe but at least this is a good sign. Last season was indeed as we saw that they really slumped by only being able to finish 12th in the standings, but let's just say that it was their time of change that we some good signs have begun to be quite visible.
Yes that's right, that indeed now what most Blues fans hope is that they expect Chelsea to be able to maintain their performance like this, they hope that there is consistency created for the next few games, although it might be quite hard to expect to win the title or even enter the top five of the standings because the season time is not long anymore, for this season yes maybe I won't have too much hope for them, but for next season I don't think there is any reason for them to slump again, after all it's time for them to restore the prestige of the club in the Premier League.
I agree with you that this season is really difficult for Chelsea to finish in the top four of the standings, so they can qualify for the Champions League next season. The most reasonable target for Pochettino squad is to finish in the Europa League zone, because we know these two matches are promising but we cannot fully believe that this is a turning point in their performance.
On the other hand, I am quite sure that this season The Blues can finish in a more decent ranking than last season, I can't imagine their spending in the transfer market being so large if they fail to improve their performance so that they can finish in a better ranking.
However, Pochettino efforts should be appreciated, perhaps his tactical qualities are now better than Ten Hag. Although we will never know in the future the Blues might slump again when faced with a mediocre club.
I honestly do not think that Pochettino has anything to do with this, players were just sick and tired of being labeled a failure and they played a lot better, they played with their heart out, they played like it was the UCL finals or EPL championship decider, they played with 100% and not an ounce lower. When you play like that, it is obvious that you are not going to get anything bad, you are going to get some decent results.
Chelsea will not continue to get these results forever, they did it, and they played well, but players won't play with 100% for every game, this was a City game and they did their best, and they did manage to score 4 goals against City, which not many teams could say in the last 5 years or so.