Hooray, a YS release! One of the best manga going on, thanks for the scans. Even with the LN being far ahead, the manga is a different enough take and executed so well still always a blast.
Though yeah downhill from here for the Empire. Author does a really excellent job of "realism" in this setting, in that no level of individual or tactical ability can defeat an overwhelming difference in logistics and raw capacity, and that politics is incredibly important to get right in terms of securing military victories. But that's very hard for any human endeavor, because the point at which you should quit with your winnings, even sacrifice a bunch of your winnings to solidify some gains, is also the point at which you're winning the most and thus people see no need to quit and sacrifice. Throughout history we can see not just countries, but companies and even individuals falling into the trap of "just a little bit more" and getting tunnel vision around solutions.
At this point probably the best thing the Empire could have (foreseeably) done would be to pull back, engage in full on diplomacy with Rus/notAmerica (ideally they'd have been doing heavy PR in the US all along, saying how they were attacked first, how they just wanted security and cared about rights etc etc), fortify, hold elections in Francois so there's a legitimate new democratic government and then sign a peace/friendship treaty with it (which would make things very hard for the US or Francois exiles, they'd then be set to trying to overthrow a democratic government with no Empire left in it). Empire though has been winning so much though that military is ascendant, but still big failure on the civilian side to have more vision. Military can't do everything.
The not-foreseeably-done option would be to stall and do an all out rush for nuclear weapons. Given what we see them pull off, and the extra of magic, it might just barely be technologically possible and within their grasp. But that'd require a constellation of unlikely factors (or knowledge of the future, but tanya doesn't have the personality/sway for that and is focused on her own efforts and place within the hierarchy). And it'd still be risky, they might not be able to do so in time at this point.