you are right that Man City might allow Gündogan to leave City because he is indeed quite old. so that Man City has the goal of releasing Gündogan and trying to find young players who have better talent to be able to bring Man City to the defending champion in the champions league.
I know maybe Guardiola has another new dream to keep winning the treble again in the new season so he sells several players who are not performing well to welcome next summer.
They have a policy to free their players who no longer want to play for them and Gundogan is their captain with lot of contributions for their club success in the last 6 years. It is fair enough and is like of recognition and respect of Manchester City for Gundogan to allow the player moving to Barcelona. It is a happy ending for the player and is helpful for the club reputation on how they treat their legendary players too.
Gundogan has good part of his career in Manchester City because he had little injuries during the time in Eithad. It is different than his last seasons in Dortmund with some injuries and he missed many matches with Dortmund.
The three names chosen by Perez are highly qualified to replace Ancelotti, Zidane and Mourinho are great coaches and have won various titles. Meanwhile, Xavi Alonso played a great role in boosting Leverkusen performance in the 2022-2023 season. Coincidentally, Alonso contract with Bayer Leverkusen also expires at the end of the 2023-2024 season, so Real Madrid can bring in Alonso for free.
Xabi Alonso still needs more time and in the Europa League semi finals against AS Roma, he shown that he lacked of ability to use alternative players to change tactics and change the match conditions. He needs more time to sharpen his tactics philosophy and flexibility to win titles. He is not a good coach for Real Madrid at the moment.
Zidane did not show any interest to manage a club after he left Real Madrid some seasons ago. He only aimed at France national coach position that is hold by his ex-team-mate Deschamps. He will not take the coach position in Real Madrid.
Mourinho looks to be a best candidate for Real Madrid. He has good successful career and in the past two seasons, he got good achievements in AS Roma with limited resources and so far in this summer, he has yet stated about his future.