Observational signatures of scalar field dynamics in modified $f(Q, L_m)$ gravity

We investigate the cosmological implications of a tanh-parametrized scalar field model in the framework of modified $f(Q, L_{m})$ gravity by adopting the form $f(Q, L_{m})=\beta Q+\delta L_{m}$ along with a scalar field energy density $\rho_\phi = \rho_{c0} \tanh(A + Bz)$. Using MCMC methods and combining $31$ cosmic chronometer data points, $15$ BAO, DESI DR2 BAO and $1701$ Pantheon+ samples, we constrain the model parameters and obtain $H_{0}=74.284^{+4.155}_{-4.275}$, $\Omega_{m0}=0.326^{+0.093}_{-0.072}$ and $B=-0.001^{+0.030}_{-0.030}$. The model predicts a transition redshift $z_{tr}=0.5914$ and a present deceleration parameter $q_0=-0.5167$, consistent with a Universe transitioning from deceleration to acceleration. We further analyze the evolution of the EoS parameter, density components and statefinder diagnostics in which all parameters show asymptotic convergence to a de Sitter phase. Additionally, we study black hole mass accretion, showing its dependence on the scalar field dynamics. This work highlights the compatibility of tanh-scalar field forms with $f(Q, L_m)$ gravity in describing cosmic acceleration and gravitational phenomena.