Kinetics Vs Thermodynamics : Apparent contradiction in the definition of Enthalpy in the two disciplines
The reason might be that while drawing the reaction energy profile, we forget to mention what energy we are mentioning in the Y-axis. The following conventions are generally used:

If reaction conditions are constant NVT, energy in Y-axis should represent internal energy.
If reaction conditions are constant NPT, energy in Y-axis should represent enthalpy.
If reaction conditions are constant $\mu$VT, energy in Y-axis should represent Helmholtz free energy.
If reaction conditions are constant $\mu$PT, energy in Y-axis should represent Gibbs free energy.
If you are looking at single molecule, the energy will be the total energy of the molecule (kinetic energy + potential energy).

In case of reactions, the last three are generally used.
Hence, the &quot;Energy&quot; Y-axis changes based on reaction conditions. In the question, it seems you might have got mixed up somehow.

Summary of the terms used:

N: No of molecules
$\mu$: Chemical potential
V: Volume
P: Pressure
T: Temperature