The season hasn't started yet and he may have started making statements to the press early. I hope it's not the same as when he was at Manchester United, where he started with losses in friendlies and then came his interviews in which he complained about players and the relationship with the players became terrible, then he made terrible signings.
Now at Leverkusen, he already had a defeat in which he conceded 5 goals in the friendly match. In 5 days, he will have another friendly match against Bochum, who were recently relegated from the Bundesliga. If he loses, it will be terrible for him.
Getting flogged by Flamengo U21 a few days ago was just a prelude of what is to come. Xhaka knows Leverkusen is finished with ETH at the club, and that's why he wants out before it's too late. Another thing is that he's not fighting to move to a bigger club, as most players would do. He's fighting to go to Sunderland, which Leverkusen is obviously bigger than. That tells me he's desperate about leaving and does not want to stick around when the ship starts sinking.
If the team's situation is as you describe, resolving these issues may take time. The team has been performing well in recent seasons, and this structure needs to continue. The new manager needs to contribute to the team and improve their performance. Achieving these goals isn't easy, but the fans and management expect it.
I believe they will not allow a repeat of what happened at Manchester United and will take action. The manager needs to address these issues urgently. It's too early to criticize the manager. We need to see how the season starts. It's clear the team isn't ready yet, but they can perform well at the start of the season.