Upon re-reading the intel entries I seem to have reached some very weird realizations about the whole Reconstruction period...
Operation Templar could not have "quickly followed" the Great War. In fact, judging from the FreeSpace 2 intelligence entries, the very earliest it could have taken place is 2358 -
More than 23 years after the Great War:
Under BETAC, the Vasudans and the Terrans maintain separate fleets under a single command structure. A warship is designated GT or GV, indicating whether it is Galactic Terran or Galactic Vasudan.
Given how the Vasudan ships in Operation Templar were designated GVD for Galactic Vasudan, it could only have taken place after the signing of BETAC, which occurred in 2358:
In 2358, delegates signed into existence the Beta Aquilae Convention (BETAC), named after the system where the constitution was drafted and ratified.
I can't believe that the HoL would have lasted 23 years in a conventional war, so it was probably something a bit more like a terrorist group with no real military strength.
Furthermore, the GTVA as we know it (ie. the GTVA as an actual government) only existed following 2358, just 9 years prior to the FreeSpace main campaign. While it had existed since 2345, the GTVA existed as nothing more than a treaty organization for trade between the Terran regional blocs and the Vasudan Imperium. During the time between 2335 and 2358, the Terran community existed as several "semi-autonomous" regional blocs. Exactly how autonomous these regional blocs is ambiguous, but personally I don't think they were hostile towards one another, simply isolationist. Whether or not the GTA existed at this point is also unknown.
So from what we can see the Vasudans probably fared better than the Terrans during Reconstruction, aside from the ever-prominent HoL threat.