I write to inquire if there can be any meaningful conversion of energy... say from rocket thrust to mechanical energy and if there are any equations governing such a transfer. Much thanks for any guidance in this regard.

There are conversion equations for one kind of energy into another, but the subject is too vast to put in this thread. If you take university classes, you would need to study physics and mathematics, which might take you through a PhD.

As an overview, think of the Sun, which is a thermonuclear explosion converting matter into energy, E=mc². Where, E is mainly photons of light which strike the earth heating its surface, making wind. Some of these photons strike leaves and are converted into chemical enery by photosynthesis. Some strike PV panels and convert directly into electricity. Some of the biomass is burned with its heat making steam to turn a turbine that generates electricity. And, the wind turns windmills to make electricity. Electricity can be converted into mechanical energy by an electric motor. Etc. There are equations for all of these processes.

You maybe interested in thermodynamics.