One thing I'd like to see is play faster. While besides Dembele we don't really have any speedster I do believe without Suarez and Busi in the lineup we can and should play much faster and with a better movement upfront.
I think we could use two formations.
1.)
4-3-3 (4-3-1-2) at home against most league teams except RM/AM, maybe Sevilla. Similar to what we've played vs Villarreal. Could also turn into 3-4-3/3-5-2 during the games with FDJ dropping back as a 3rd CB and pushing both FBs higher. We could also use this system away against teams expected to sit back as Cou/Puig could add more creativity in midfield to easier break them down.
Depay/Fati and Griezmann playing as inside forwards with Messi dropping back but he shouldn't go all the way to mid line anymore with (hopefully) better service provided by midfield. Ideally he should stay as close to goal as possible as he's still the best finisher in this team.
I know width is a problem here as we don't have true wingers (besides Dembele who can't be counted on much) and FBs are far from great but I think both Fati and Depay could be good in that inside forward role on the left. And in small samples last season Griezmann also looked better playing on the right with a freedom to move more central when Messi drops deeper. Trincao could also play well in that role I think.
2.)
4-2-3-1 for tougher home games (RM/AM) and away games against teams who could hurt us in counters. I'd like to play with a lower backline (15-20m inside our half instead of having 10 players in their half when we can't even defend with offside line anymore) so Pique's and Lenglet's lack of speed won't be as exposed on open field. Shorten the playing field around the half line and if (by some coincidence) Dembele will be available for important games (at least from the bench) use his speed to get behind opponents defenses. He's not as useful against parked busses so we should help creating space for him when he's playing. And while Depay, Fati and Griezmann are not as fast as Dembele they could also still cause troubles with a good off the ball movement waiting for Messi's through balls. But most important in those games is to surround Messi with mobile players so we won't struggle defensively as much and at the same time also create more passing options for him offensively.
I've included Memphis and Gini because I believe we'll get them. I didn't include Lautaro as I (thankfully) don't see us having enough money to buy him and he'd also cause us more problems than solutions anyway. And I also didn't include new players in defense as I don't expect many changes there. At least not important ones which would allow us to play much differently (so a faster CB instead of Pique and a big improvement on one or both FB positions). Maybe Cancelo will come instead of Semedo and E.Garcia for Todibo but this won't change much in grand scheme so I was mostly focused on midfield and attack. But those are also very important for a whole defensive structure so if we'll improve there I believe defense will also look better.
Also, sadly I just don't see a spot for Pedri in the lineup next season with Coutinho staying and possible signings (Gini, Depay) both also (in)directly influencing his playing time so unless Koeman sees things differently and can provide him enough minutes I think we should loan him. Gladbach would be a great loan destination if they're still interested.