Milan doesn't look like they are in a hurry to bring a new manager after parting ways with Pioli. I assume they just decide to wait for Euro 2024 to end. Maybe they even want to watch some managers here to add them to the list according to the performance. 
There are always good managers out there. Making the right choice is the most difficult thing for the long term. Milan likes to bring Italian managers more often than the ones from other nationalities. They might have entered the race as well if Napoli didn't finish Conte deal quickly. After Allegri and Ancelotti, this was the first time they went for the long term with the same coach. I'm curious about whether they will find a manager to work with for as long as Pioli's time.
There are always good managers out there. Making the right choice is the most difficult thing for the long term. Milan likes to bring Italian managers more often than the ones from other nationalities. They might have entered the race as well if Napoli didn't finish Conte deal quickly. After Allegri and Ancelotti, this was the first time they went for the long term with the same coach. I'm curious about whether they will find a manager to work with for as long as Pioli's time.
Milan is a club that doesn't change coaches very quickly. Because the Milan management knows very well that any coach needs time to adapt to the players in his team. It is foolish to think that the performance of the team will improve immediately with the change of coach. Moreover, most of the times we see that the performance of the teams becomes unstable after the change of coach. This is why the Milan management is not interested in a quick coach change.
Stefano Pioli coached Milan for the last 5 seasons. I wouldn't say that Milan's performance with Pioli was poor. But I look forward to seeing if the players can adapt to the likes of Paulo Fonseca. Paulo Fonseca coached Roma and Lille in the last few years. With Paulo Fonseca, Roma and lille's performance was strong, no way to say that.