Is the identification and reduction of employees, whether by study or personal estimation, considered a severance of their livelihoods and thus unlawful (haram), especially if not doing so would expose the employee himself to dismissal?

There is no harm in you carrying out the requested task, and no sin will befall you for dismissing someone whom the work does not require, because the cessation of provision is not in the hands of humans. Allah alone is the Provider. The Messenger of Allah, peace and blessings be upon him, said: "Indeed, the Holy Spirit inspired in my heart that no soul will die until it completes its term and consumes its provision." And whoever's provision from a job ends, provision will come to them from another door.