  Using the variational principle, we systematically investigate the mass
spectra and wave functions of both $1S$ and $2S$ state heavy pseudoscalar $(P)$
and vector $(V)$ mesons within the light-front quark model. This approach
incorporates a Coulomb plus logarithmic confinement potential to accurately
describe the constituent quark and antiquark dynamics. Additionally, spin
hyperfine interactions are introduced perturbatively to compute the masses of
pseudoscalar and vector mesons. The present analyses of the $1S$ and $2S$
states require the consideration of mixing between them to account for
empirical constraints. These constraints include the mass gap $\Delta M_{P} >
\Delta M_{V}$, where $\Delta M_{P(V)} = M^{2S}_{P(V)} - M^{1S}_{P(V)}$ and the
hierarchy of the decay constants $f_{1S} > f_{2S}$. We find the optimal value
of the mixing angle to be $\theta = 18^{\circ}$, significantly enhancing the
consistency between our spectroscopic predictions and the experimental data
compiled by the Particle Data Group (PDG). Furthermore, based on the predicted
mass, the newly observed resonance $B_J(5840)$ could be assigned as a $2^1S_0$
state in the $B$ meson family. The study also reports various pertinent
observables, including twist-2 distribution amplitudes, electromagnetic form
factors, charge radii, $\xi$ moments, and transition form factors which are
found to be consistent with both available lattice simulations and experimental
data. In addition, our predicted branching ratios for the channels of $B^+
\rightarrow \tau^+ \nu_{\tau}$ as well as rare decays of $B^0$ and $B_s^0$
appear in accordance with experimental data.
