We perform the first simultaneous Bayesian inference of the temperature-dependent heavy-quark spatial diffusion coefficient $2\pi T{\mathcal{D}}_s$ and the scaled jet transport coefficient $\widehat{q}/T^3$ in the heavy flavor sector, utilizing $D$-meson nuclear modification factor $R_{\text{AA}}$ and elliptic flow $v_2$ data from $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02\text{TeV}$. The analysis employs a unified improved Langevin transport model that incorporates both collisional and radiative energy loss, followed by coalescence plus fragmentation hadronization. The posterior distributions of the parameters of $\widehat{q}/T^3$ and those of $2\pi T{\mathcal{D}}_s$ are well constrained, and are found compatible with the results of theoretical models, other experimental data extractions, especially with the $\widehat{q}/T^3$ extraction using light flavor, large transverse momentum observables. The $30\text{–}50\%$ centrality data provide significantly stronger constraints than the $0\text{–}10\%$ data. The extracted ratio $\widehat{q}/\kappa$ between the quark jet transport and heavy-quark diffusion coefficients exhibits a nonmonotonic temperature dependence, deviating from the value 2 estimated from the definition, with a value interval spanning 0.25–0.8 corresponding to the mean values of the inferred parameters in the temperature range. This work establishes a data-driven quantitative relationship between these two fundamental transport properties in the $D$-meson observables, offering crucial insight into their interplay in the strongly coupled medium.

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• Collective flow
• Jet quenching
• Jets & heavy flavor physics
• Relativistic heavy-ion collisions