This is not a trolley problem in that there is sequence involved:
1: Tuvok and Neelix alive before transport
2: Tuvok and Neelix dead and a new rational being in their place. This being had a moral blank slate and are thus blameless for the circumstances of creation.
3: Janeway decides that the speech she gave to the Vidiians was just hot air and that she will kill Tuvix to get the original two back. (Non lethal ways were explored, but quickly abandoned)
4: The blameless being makes an articulate case for their life, and even addresses the “needs of the many” argument by stating the truth: the other two are gone and the new being is there. (Raw, unalloyed utilitarianism is problematic at best, just ask the people of Omelas Majalis)
5: The doctor straight up says that the procedure is unethical and refuses to do it.
6: Janeway does it anyway.
Calling it a trolley problem is reductive and inaccurate.