Yes that's right, and the impact of the injury was very disruptive to his performance on the field so that Fati could not fully display his best performance as usual. his career seemed to stagnate there especially followed by many competitors for him at Barcelona. I think this is indeed the best decision for him and Xavi also said this decision was none other than so that he could play full minutes without intense competition at Brighton and it was also for the good of Fati. Obviously I also don't think Fati would turn down an offer to play in the Premier League, and one of the reasons for his departure is because he really believes in De Zerbi.
It's just a loan, so Barcelona didn't lose anything if Ansu Fati can perform and regain his confidence back. Maybe De Zerbi willing to pay big amount of money to sign Ansu Fati, but it's an another discussion in the future.
Barcelona also don't have any problem with their squad, Yamal is replacing Dembele and Felix is replacing Ansu Fati.
Even though they are only on loan, young players like Ansu Fati could be a good strategy for Barca to develop their talent without burdening the club with the risk of long-term injury. If Ansu Fati can fully recover and restart his career well, Barcelona can get quality players without having to spend big transfer fees. So, in this case Barcelona will not lose if Ansu Fati returns to perform well. and this is an advantage for Barca
However, it is possible that other coaches or clubs like De Zerbi are interested in buying Ansu Fati in the future. If Ansu Fati performs brilliantly during his loan spell and De Zerbi is willing to spend big, that could be an option in the future.
and I think Barcelona have replaced Ansu Fati with Felix and Dembele with Yamal in their squad. It is a common decision in the world of football when a club has to adapt its squad based on the physical condition of the players and the needs of the team.