It is painful to be under even a hint of suspicion, especially when you know you have done nothing wrong and you value doing your work honestly. That sense of being looked at differently, with an implication hanging over you, can feel heavy and unjust.
Scripture gives a clear standard for how accusations are to be handled. The law required that a matter be established by two or three witnesses, and that same principle is repeated in the New Testament that an accusation is not to be received without two or three witnesses. A hint, an allusion from a friend, or a general suspicion is not a witness. God established that standard because reputations are fragile and can be badly damaged by talk that is not proven, sometimes even by people who are simply repeating what they heard or who act out of other motives. The Bible treats bearing false witness as a serious sin, and shows that God Himself is the ultimate witness who sees what is done in secret, even where cameras cannot see or where they do see.
It is good that there are cameras in your workplace, because truth matters and God is a God of truth. Pray that what actually happened will come to light clearly, that the missing item will be found or the record will show plainly what took place, so that your integrity is evident to all. In the meantime, continue to walk faithfully as you have been, doing your rounds with a clear conscience before the Lord. The Lord knows your steps and your honesty, and He cares about your name and your peace of mind.
I am praying for you, that God will bring the facts into the open, that any false implication against you will be removed, that your supervisors and coworkers will see the truth and deal fairly, and that you will have peace and freedom from anxiety while you wait. May the Lord guard your heart, keep you from bitterness toward those who have suspected you, and let His truth be your vindication.
Father, in the name of Jesus, You see all things and know this situation completely. You know this worker's heart and actions. We ask that You cause the truth about what is missing to be clearly revealed, that what the cameras have recorded or what further searching shows will make it plain. Clear this person's name from any wrong implication, protect their reputation, and give them peace. Help them to continue to work with honesty and grace, and to trust You to defend them. Amen.