I think, as suggested, that there is a political reason for a TL12 Imperial Army could have a lot of juice. Will they get curb stomped? Yes, they will. Will there be political fallout? Also yes. Fun galore there.
The Imperial Army is off board at the start of the war, it doesn't appear in force until the reinforcements turn begins. The Imperium does not maintain Imperial Army units on worlds in the Spinward Marhces, they are on Efate because they are fighting a war for example. There are a few waystaions, there are lots of IN bases, they stockpile the supplies. The regular Imperial Army is deployed via the IN during the war, with all the logistics they need.
They are TL15, with a minority of TL14.
Local worlds provide colonial forces that are drafted by the Imperium, and also planetary troops that can never leave their own planet. Then there are the houshold troops of the subsector dukes.
The question if have is why they station the main army units so far from where they have to know the next fight is going to be?
Because of comm lag, there is no god view.
Because they don't know where the fight will be. Which worlds are the Zhodani going to land armies on rather than bombard into submission then send in token troops to occupy?
Because if they station the Army too close to the likely conflict zone the Zhodani can make a beeline and nuke them from orbit - unless you also have a defensive fleet, in which case you now have a fortress world....
The Army, much like the majority of the Navy, is off board awaiting the Zhodani to make their play. Local forces and regular units can do no more than delay, the game doesn't really get going for the Imperials until their reinforcements start to take the field.
Anyone that is shocked that the Zho will attack hasn’t been paying attention. Why not have them stationed within a dozen parsecs of the border? Safe from immediate attack but close enough to respond. Or 20 parsecs if that is still too close.
They are, but it takes time for the communication of the assault to travel those 12 parsecs, minimum 2 weeks, in reality longer since it takes time for the news of the invasion to be relayed from the Zho jump off point to the nearest IN base and then via fleet courier) next bottleneck is some time to organise and embark troops, then at fleet movement speed 3 to 4 weeks to get them to the conflict zone, longer to get to where ever the Zh are now since your intel is a month out of date.
Meanwhile teh Zhodani have jumped