  This article presents a new model for anisotropic compact stars that are
confined to physical dark matter in the background of $f(T)$ teleparallel
gravity. The model is based on the equation of state (EoS) of the bag model
type and the Bose-Einstein dark matter density profile. The derived solutions
meet the energy conditions, the causality conditions, and the required
conditions on the stability factor and adiabatic index, indicating that they
are physically well-behaved and represent the physical and stable matter
configuration. We also determine the maximum mass, surface redshift, and
compactness parameter at the surface. Interestingly, all of these numbers fall
within the specified range, supporting the physical viability of our proposal.
Additionally, the various masses that are derived for varying the model
parameter $k$ correspond to five compact, realistic compact objects, including
LMC X-4, Her X-1, 4U 1538-52, SAX J1808.4-3658, and Cen X-3. We have also
illustrated the radially symmetric profiles of energy density and the moment of
inertia for non-rotating stars.
