Federation soldiers like Gomez literally had to take a leave of duty so they could fight alongside the League Militaire, so the higher ups were either too out-of-touch with how dangerous Zanscare was, or were bogged down with off-screen space politics. And when the EF did eventually start doing shit, they pretty much immediately accepted a ceasefire, which did nothing but let Zanscare build up their forces.
I mean, it's not the first time they did absolutely nothing for most of a conflict. A lot of stuff post-OYW is them not giving a fuck, like with the Titans, then Char's Neo Zeon, then Cosmo Babylonia. Zanscare was just another extension of that, where they only ever started taking action at the very end.