Is what I and my colleagues did—writing a paper to the company demanding the removal of the unjust manager, after which I was chosen to oversee the department—considered an injustice to this manager?

Anyone who assumes a position or authority must fear Allah concerning those under their charge, treat them kindly and gently, and not be harsh with them. For whoever is in charge of the Muslims' affairs and causes them hardship, the Prophet, peace and blessings be upon him, prayed for hardship upon them. And whoever treats them gently, he prayed for gentleness upon them. This applies to anyone who assumes any responsibility, no matter how minor. If the former manager was as you described, there is no sin in complaining about him and removing his harm from you and your colleagues.