Is recording all conversations taking place in the institution during the manager's absence, without anyone's knowledge, considered eavesdropping and an abuse of power over others, given that this occurs in the workplace which is under the manager's responsibility to know what transpires during his absence?

Your recording of employees' conversations after your departure involves several religiously prohibited acts: 1. Spying (Tajassus): This is forbidden by Allah's saying: ﴿And do not spy﴾ [49:12]. It is not permissible unless there is a strong presumption that a crime will occur and can only be prevented by spying. 2. Ill-suspicion (Su' ad-Dhann): Your action indicates ill-suspicion towards the employees, and ill-suspicion towards Muslims is forbidden by Allah's saying: ﴿O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin.﴾ [49:12], and by the Prophet (peace be upon him) saying: "Beware of suspicion, for suspicion is the most mendacious of speech... (the Hadith (definition))." 3. Listening to speech they dislike being heard: The Prophet (peace be upon him) said: "Whoever listens to the conversation of people while they dislike it, or flee from him, molten lead will be poured into his ears on the Day of Resurrection."

These prohibitions are sufficient to render your action forbidden.