but it does occasionally engage in ground campaigns of conquest of (technologically unsophisticated) alien planets
How do they reconcile this with being a union of voluntary members? Most people today would object to the enslaving of alien civilisations so how are the invasions being sold to the public?
Main limiting factor is how big is this political body? Even with magical star wormholes to move about with we are nowhere near any magic tech that will enable us to terrorform planets on the scale to have a meaningulful star empire. Unless liveable planets are far more abundant than currently thought the main population centre is still going to be stuck at the bottom of the earth gravity well with only minor colonies numbering in the dozens for the resources/science projects.
Ultimately with the tech available within a couple of hundred years you’re going to have maybe a few dozen light patrol ships that double as rescue ships for the civilian traffic and some transports for supplies to the colonies/research outposts. The fact they have encountered aliens may mean they have some larger ships kept near earth but I'd imagine their limited to large missile racks with engines bolted on as an offensive platform and maybe orbital missile platforms with lasers bolted on for Earth.
In terms of conquering alien worlds, unless their sparsely populated I don’t see how you can have that many men and materials being transported to pick on some primitive society without magic means of getting out of the gravity well. The shear cost of running an invasion on a stellar distance would preclude it unless there’s special alien tech available (in which case their not the defenceless primitives) or the aliens can simply be intimidated by orbital strikes into surrendering which isn’t that believable, people at home would likely object to genocide.
At least enough to effectively move several hundred thousand troops between planets on a single trip.
How are these massive troop concentrations getting out of the gravity well? How are they kept supplied? Why is a peaceful government’s population ok with invading alien worlds light-years away?
How far away from the sun are the wormholes in Alderson FTL? Could mines/stations be constructed near them or is it too close to stay there for long.
Get busy living or get busy dying... unless there’s cake.