The records don't show how many wars the Empires of Gashikan and the Julian Protectorate have waged. In some ways they have always been at war, whilst in others relations are more normal.
The relationship is somewhat like the 3I/Zhodani one, with the added flavour of immediate slavery for any Vargr that end up inside the TEG (although non-psionic humans may regard their treatement by the Zhodani as effective slavery).
The TEG is like the USSR in that it is failing economically and the original anti-Vargr fervor has been replaced by a default bias that is rarely ever questioned.
In campaigns I've run the main problems for players has been the failure of the TEG, resulting in pocket empires being created that often want to wage war on their former comrades and enemies alike, often with ex-TEG war machinery.