Is it permissible to compensate the state for what has been consumed of its private property in ways that might benefit other employees for personal gain? Is it permissible to compensate the state with property previously used in one's home? Is it permissible to drink the tea and coffee available at the workplace, which are part of the institution's expenses?

You must absolve yourself of anything taken unlawfully by returning it or estimating its value and depositing it into the workplace's fund. This includes tools used for personal matters. As for placing used cups in the workplace kitchen, that is not sufficient to ensure their damage. There is no harm in drinking tea and similar items provided by the workplace with its permission.