  Dark energy is the component in the present Universe with the greatest
abundance, and it is responsible for the accelerating expansion of the
Universe. As a result, dark energy is likely to interact with any compact
astrophysical object [Muhammad F.A.R. Sakti and Anto Sulaksono, {\it Phys. Rev.
D} {\bf 103}, 084042 (2021)]. In present paper, we propose a model for a dark
energy star made up of dark and ordinary matter in which the density of dark
energy is proportional to the density of isotropic perfect fluid matter. In the
context of general relativity, the model is derived in the curved
Tolman-Kuchowicz spacetime geometry [Tolman, Phys Rev 55:364, (1939);
Kuchowicz, Acta Phys Pol 33:541, (1968)]. Here, we look at how dark energy
affects stellar mass, compactness, and equilibrium etc. The physical parameters
of the model e.g., pressure, density, mass function, surface redshift etc. are
investigated, and the stability of stellar configuration is studied in detail.
The model has interesting properties because it meets all energy criteria and
is free from central singularities. The maximum allowable mass has been
obtained from our model with the help of $M-R$ diagram. We analyse many
physical properties of the model and checked that it meets all regularity
constraints, is stable, and therefore physically realistic.
