The solution was to replace the Desktop Flow Input variable of Password (with default set to the actual password) and just have the raw string of the password. This seems far from best practice but the flow should not work when building it but fail when being called in Unattended RPA mode. The stress of this not working and breaking a production workflow means I will be slightly less secure now with the hope that this behavior is corrected in a future update.
I "debugged" by taking using the Take Screenshot method in Desktop Flows after each step in the flow, running it Unattended, then going back to see that the password field was not being populated. There has to be a better way to do this I am not aware of, but it worked for me.