Maybe this motivation occurred when Xabi saw the achievements of Pep Guardiola who always stayed at Manchester City and ended up achieving success and this can be done by Xabi when he can get a good start, the positive trend will definitely continue.
Does Leverkusen's owner have the same monetary power as City Group? I'm pretty sure one of the reasons why Guardiola stays is because he can buy the players that he wants regardless of the price. While you can compete with Bayern like Dortmund does by buying young players with tons of potential, I'm pretty sure it will be stressful. Just look at Jurgen with Liverpool.
Going to Liverpool could be a good thing but I don't know if he would want to go to Anfield if Jurgen Kloop is not there from next season.
Whether he wants a move to Liverpool or not, I believe some fans Liverpool fans don't think highly of this transfer. I believe some of them think he is too injury-prone, and fear that he end up like Thiago where he only plays regularly for one season and then has a long-term fitness issue. I'd not be surprised if they stick with their youth players instead of buying new players even if they are experienced like Kimmich in the next window tbh.