The ALICE collaboration reports the azimuthal-anisotropy coefficient of prompt , , mesons and the first measurement of of prompt baryons in semicentral collisions at a center-of-mass energy per nucleon pair of = 5.36 TeV. The D mesons and baryons are reconstructed in their hadronic decays at midrapidity ($\yrange0.8$) in the transverse-momentum interval 0.5 $<$ $<$ 24 . Similar values are measured for and , while a hint of a difference ($2.6\sigma$) emerges between and mesons in the $1 <\pt < 5~\GeVc$ interval. A larger for baryons with respect to mesons is observed with $3.7\sigma$ significance for $4 < \pt < 12~\GeVc$, providing evidence for the partonic origin of charm-hadron and hadron formation via quark coalescence. This interpretation is further supported by comparisons with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium.