No, it’s one from each group.
First they adjust the groups from Worlds to remove anyone who isn’t skating in the upcoming season, is skipping GP, is no longer eligible (ex: split couple switching countries and forced to sit out the Fall for any reason), or whose Fed doesn’t enter them for GP consideration. (Happened to both Sandhu and Sokolova when they would have been guaranteed spots.)
Then the hosts draw for the order in which they choose for each discipline, after host picks are assigned. I think maybe 2 or three times there have been exceptions where a host has chosen more than one from the same group, but it’s extremely rare and bad strategy except for ticket sales.
I’m not sure where returning skaters and split couples that aren’t chosen by the hosts fit into this, especially since they aren’t guaranteed anything.
The skaters in top 3 and (probably 4-6) get preferences in order of placement, but host nation picks overrule those. For example, Malinin could say that he wants SA and France, but the French Fed can laugh and assign Siao Him Fa to France, thus getting their Top 3 skater.
After every host has one of the Top 3, then they each get one of 4-6. If any of 4-6 is a host pick, then that host skips selecting in that round because they already have one from 4-6. They do the same for 7-9, then 10-12 for singles or 7-10 for Pairs and Dance.
Then they go through other groups that are guaranteed one (SB 24, WS 24). Hosts can choose to give anyone eligible two, as long as everyone guaranteed a spot gets their guaranteed spots. Mathematically it’s possible for there to be too few spots in Pairs due to the 18 host picks in a field of 8/GP but it would be a very, very, very long shot.
The irony is that, if 4-6 get their preferences, #4 might get both of their choices as top of their group, while #3 gets what #1 and #2 don’t want, unless one of those spots is a wanted host pick. Similarly, a host that chooses last has to take whoever is left over in a group, while the next host to pick gets their choice of any non host picks in the next group.