You are correct in your information on the Cadet Corps. However, Count Langeron, a French emigre in the Russian service who rose to general officer rank noted in 1796 'that most officers were not well educated and trained: there were three cadet corps preparing young men to be officers in the army, but the number of men in these establishments was limited, too small for the army, and the usual way for young nobles to become officers was to enlist in the army as NCOs and wait for commission.'-Alexander Zhmodikov and Yurii Zhmodikov, Tactics of the Russian Army in the Napoleonic Wars, Volume I, page 2.
On page 26 of the same volume regarding the reforms of Paul I, it is noted that he reorganized the Artillery and Engineer Cadet Corps as the Second Cadet Corps, 'which now gave no special artillery education.'
Page 63 of Volume II states that 'in 1800-1806, there was no military educatinal establishment in Russia that provided any special artillery education, except a class in the Guard Artillery.' Between 1806 and 1812 two small officer classes were added to the training company in the Guard artillery, which was an improvement, but not on the scale that was needed.
As I have said before, the Russian artillery arm improved steadily after 1805-1806 but it was not on a par with the French, British or French artillery arms until after the end of the period. For French artillery education I highly recommend Ken Alders Engineering the Revolution for the curriculum of the French artillery schools both before the advent of Gribeauval and after. The French first founded an artillery school in 1679 at Douai and the French artillery educational system was formalized in 1720. Most of the European artillery advances during the period were French, and the Austrians used the French model when establishing their artillery school in the 1750s.