From a quick look, The Coming Storm history (page 5 sidebar) indicates that for general history information for Sartar you should look at Sartar - Kingdom of Heroes. It's history info is generally more local in scope.
The history in S:KoH is set out in fairly broad strokes though. For the period you nominated, the table on page 272 has:
1590 Tarsh is finally pacified - so arguably the impact on Sartar involves refugees, defending and reinforcing the border and perhaps supporting the Wintertop exiles around Kero Fin.
1591 Lunar invasion defeated by an alliance of Satrar and the Holy Country.
1602 Fall of Sartar
1605 Lunar invasion of the Holy Country. Building Wall battle.
S:KoH has lots of details about locations and clan structures though, so that might be helpful if you have it.
Going off-canon (at least I imagine it is no longer canon) the article 'Dragons Past 1' from Different Worlds #28 indicates that there is the annhilation of the Maboder under the fangs of the Telmori in 1606, followed by the reprisals of Jomes Wulf and the Lunars known as the Conquest of the Telmori in 1607.
After 1602 there would have been Lunar agents seeking out and eliminating anyone who was a blood relation of the Sartar royal family.
From memory,there was also the failed attempt by the Lunars to launch an invasion of Prax in 1608. The Lunars ended up having to give significant concessions to the priestesses of the Paps to be allowed to return alive.
This indicates that there would have been a significant amoount of military activity in Sartar, both to pacify it and to launch invasions in 1605 and 1608.