Is there any Sharia-related reservation concerning the supplication which states: "O Latif (the Subtle One), by the Power with which You ascended over the Throne, and the Throne did not know where Your abode on it was, but You sufficed me in such and such"?

Allah's استواء (ascension/establishment) over His Throne is one of His attributes, about which He informed us in the Qur'an. There is no harm in supplicating to Him by His established Names and Attributes. As for the Throne's unawareness of Allah's استواء, there is no praise in that, as it is an inanimate object. It is better to suffice with the supplications transmitted in the Qur'an and books of adhkar (remembrances).