Gundogan's transfer to Barcelona allowed me to reflect on his decision to join the club despite Manchester City's desire to keep him. He could want to try another league in a new setting and see how it feels. He's still an energetic and good midfielder, and he'll undoubtedly strengthen Barcelona's midfield, but he's already created an opening that Manchester City must fill as quickly as possible. With Barcelona's current squad depth, he might win the La Liga with them before his contract expires.
Gundogan is like Lewandowski and they wanted to experience tiki-taka at its origin, Barcelona. They both grew up in Dortmund and had some seasons with Pep Guardiola, Lewandowski worked with Pep in Bayern Munich and Gundogan worked with Pep in Manchester City. I don't know Gundogan asked for advice from his ex-team-mate Lewandowski about Barcelona before he accepts their offer but I guess it is attractive to play in Barcelona if a player loves tiki-taka.
Gundogan improved a lot in the last season and scored many goals for Manchester City. He will help young midfielders in Barcelona like Gavi and Pedri as they need to learn how to play attacking more directly and make more distant shots like Gundogan.
Kevin De Bruyne will replace Ilkay Gundogan who moved to Barcelona. De Bruyne will be Manchester City's main captain next season, but Pep Guardiola may still be hoping for a worthy replacement.
De Bruyne plays at a different position than Gundogan and I don't think Pep will use De Bruyne to replace Gundogan. The midfielder will miss some early months of a new season by the injury he got from the Champions League final match. Pep and Manchester City even have to plan to replace De Bruyne in next few seasons.