Question: Nikolay Arsenyev served during the Kościuszko Uprising after which war?

Context paragraphs:
Warsaw Uprising (1794): The Warsaw Uprising of 1794 or Warsaw Insurrection (Polish: "insurekcja warszawska" ) was an armed insurrection by the people of Warsaw early in the Kościuszko Uprising.  Supported by the Polish Army, the uprising aimed to throw off control by the Russian Empire of the Polish capital city (Warsaw).  It began on 17 April 1794, soon after Tadeusz Kościuszko's victory at the Battle of Racławice.

Józef Niemojewski: Józef Niemojewski (of Rola coat of arms) (born July 4, 1769 in Śrem - died July 16, 1839 in Rokitnica) was a Brigadier General of the Duchy of Warsaw, Major General of the Polish insurrectionist forces in Wielkopolska during the Greater Poland Uprising (1794) and the Kościuszko Uprising, Brigadier General in the Grande Armée of Napoleon Bonaparte and elected starosta of Śrem eldership.

Tadeusz Kościuszko: Andrzej Tadeusz Bonawentura Kościuszko ("Andrew Thaddeus Bonaventure Kosciuszko"; February 4 or 12, 1746 – October 15, 1817) was a Polish-Lithuanian military engineer and a military leader who became a national hero in Poland, Lithuania, Belarus, and the United States.  He fought in the Polish–Lithuanian Commonwealth's struggles against Russia and Prussia, and on the American side in the American Revolutionary War.  As Supreme Commander of the Polish National Armed Forces, he led the 1794 Kościuszko Uprising.

Kościuszko Uprising: The Kościuszko Uprising was an uprising against Imperial Russia and the Kingdom of Prussia led by Tadeusz Kościuszko in the Commonwealth of Poland and the Prussian partition in 1794.  It was a failed attempt to liberate the Polish-Lithuanian Commonwealth from Russian influence after the Second Partition of Poland (1793) and the creation of the Targowica Confederation.

Nikolay Arsenyev: Nikolay Dmitrievich Arsenyev (Russian: Никола́й Дми́триевич Арсе́ньев , b. circa.  1739 – d. 1796) was a major-general of the Russian Empire, who served during the reign of Catherine the Great (r. 1762–1796).  He fought at the Russo-Turkish War of 1768-74, the Russo-Turkish War of 1787-92, the Polish–Russian War of 1792 as well as the Kościuszko Uprising.

Jan Kiliński: Jan Kiliński (1760 in Trzemeszno - 28 January 1819 in Warsaw) was one of the commanders of the Kościuszko Uprising.  A shoemaker by trade, he commanded the Warsaw Uprising of 1794, an uprising against the Russian garrison in Warsaw.  He also became a member of Polish provisional government.

Polish–Russian War of 1792: The Polish–Russian War of 1792 (also, War of the Second Partition, and in Polish sources, War in Defence of the Constitution (Polish: "wojna w obronie Konstytucji 3 maja" )) was fought between the Polish-Lithuanian Commonwealth on one side, and the Targowica Confederation (conservative nobility of the Commonwealth opposed to the new Constitution of 3 May 1791) and the Russian Empire under Catherine the Great on the other.

Nikolay Tuchkov: Nikolay Alexeivich Tuchkov (16 April 1765 - 30 October 1812, Yaroslavl) was a Russian general of the Russo-Swedish War (1788–1790), the suppression of the Kościuszko Uprising and the opposition to the French invasion of Russia.  He rose to the rank of lieutenant general and commander of an infantry corps.

Proclamation of Połaniec: The Proclamation of Połaniec (also known as the Połaniec Manifesto; Polish: "Uniwersał Połaniecki" ), issued on 7 May 1794 by Tadeusz Kościuszko near the town of Połaniec, was one of the most notable events of Poland's Kościuszko Uprising, and the most famous legal act of the Uprising.  It partially abolished serfdom in Poland, granting substantial civil liberties to all the peasants.  The motives behind the Połaniec Proclamation were twofold: first, Kosciuszko, a liberal and reformer, believed that serfdom was an unfair system and should be ended; second, the uprising was in desperate need of recruits, and freeing the peasants would prompt many to enlist.

Wilno Uprising (1794): The Wilno Uprising of 1794 or Vilnius Uprising of 1794 began on April 22, 1794, during which Polish and Lithuanian forces led by Jakub Jasiński fought Russian forces occupying the city during the Kościuszko Uprising.  The Russians were expelled from Wilno (Vilnius), and thanks to Jasiński's skill, no casualties were sustained during the bloodless uprising.

Supporting paragraphs: Nikolay Arsenyev Polish–Russian War of 1792
Answer: the Russo-Turkish War of 1787-92