In open quantum systems, the description of the energy transfer processes under general beyond-unitality quantum channels is made difficult by the lack of operative quantum definitions of work and heat flux, and by the limited practical access to information on the reservoir. We experimentally investigate the energy transfer processes involving a Nitrogen-Vacancy center spin in diamond, where stochasticity and irreversibility are introduced by the combination of quantum measurements, a genuinely quantum mechanical feature, and a tunable dissipation channel. With this novel toolbox, we verified quantum fluctuation relations both for a spin qubit and a spin qutrit. In the case of a qubit, we formulate the quantum exchange relation encoding the missing reservoir information in the energy scale factor defined by the system out-of-equilibrium steady-state properties. In a second experiment, we consider a qutrit dynamics conducting to non-thermal stationary states: here, we show that the dissipative dynamics can be characterized by introducing a unique energy scale factor obeying a general energy exchange fluctuation relation only defined in terms of the initial and asymptotic (stationary) states, and that the quantum Jarzynski-Sagawa-Ueda relation is valid by modeling the dissipation as an intrinsic feedback process.