The team has played decently since that Cadiz game overall, it is correct.
I don't demand a lot better results than that, and I don't think Puig, or any other player, would be a guarantee for better results.
But don't let the results fool you into thinking Barcelona have been great, or that Koeman has been great. Remember Barcelona have had the better team in every game they have won, still they have needed luck in quite a few of them, sometimes against teams I never even heard of before... They lost the supercopa very unnecessarily and CL was an embarrasment, and Koeman has made many strange decisions, often just worsening the team. Messi is the goat and he has shown it, other players also saved Koeman multiple times.
At least twice since that Cadiz game the consensus here have been that Barcelona obviously needs to get rid of Koeman.
Regarding Puig, it is not like he is coming on and playing terribly one game and then just OK the next; he is showing with every appearance that he is deserving of more minutes. Based on what we see in the games, I cannot understand how anyone can say he isn't good enough. Of course there might be things going on in training or otherwise that I don't know about, but the situation is strange.
What is good is Koeman does what he thinks is best, I respect it and think it is necessary and what Barcelona needed. He is not overperforming with this Barcelona though, and he is certainly not above critique. And if Puig needs to do something, it is not to play better the minutes he gets, because I never saw a player convince more with so little playing time.