Is listening to the person next to the worshiper to confirm the position of the rak'ah considered spying?

There is no harm in listening to what the person next to you recites during prayer with the intention of emulating them. This is not considered forbidden spying. The blameworthy spying is searching for people's faults and mistakes. It has been authentically reported that the Prophet, peace and blessings be upon him, listened to Abu Musa al-Ash'ari's recitation at night while he was praying without his knowledge, and Zayd ibn Khalid al-Juhani observed the Prophet's prayer to emulate him.