Note that Alpha Centauri is just 4 ly from Sol, so I think that both sides tried some sub light communication with each other. GTVA constitution grants all power in human space to GTVA, while from EA point of view GTA should be under their control. I don't think that both sides would not appreciate it. It's like USA constitution would grand US power over Great Britain while GB still tread USA as it's province.
IMO EA would know at least about NTF uprising and might see GTVA as incompetent and weak, so in their view they actually might doing this to sake of human kind, not because they like war. (if it's accurate in both old and new Inferno Vasudans tried to stay away from conflict and EA tried not to provoke Zods).
Additionally Earth/Sol saw civil war after node collapse and it was core colonies (so they supose to be most loyal) who opened fire first. No suprise that they see rest of GTA outside of Sol as very big thread to their existence and GTVA constitution doesn't help it.
IMO EA is UEF from BP with Tevs mentality from from BP2 and very big sticks to use that mentality
There is one problem - EA must be aware of 80 Shivan Juggernauts so it's still stupid to wage war with GTVA, but maybe they are confident that Icanus + regular fleet would be enough to deal with them (again stugid assumption as Collossu was so epic cluste**** that it made through 4 LY distance for sure).