If Boehly is willing to just throw money around, I can see the logic behind buying FDJ this window rather than waiting until next summer once Kante/Jorginho have their contracts expire. A lot of excellent midfielders have needed a season or close to adapt to the speed and lack of time in the PL - Rodri, Partey, Jorginho, Gundogan, and Kovacic all didn't really hit stride until their second year, even Fabinho needed a bedding in period. There's a good argument for letting FDJ integrate slowly this year as a way to set him up for next year.
Chelsea fans will no doubt dislike this part, but I also just don't think Gallagher has a future under Tuchel in a two man midfield. To me he just doesn't have the positional discipline or technical level to play CM for a team that wants to dominate possession and needs a lot of tactical nous out of the players in that position.