The ATLAS detector at the Large Hadron Collider has been used to measure jet substructure modification and suppression in Pb+Pb collisions at a nucleon-nucleon center-of-mass energy $\sqrt{s_{_\mathrm{NN}}}=5.02~\mathrm{TeV}$ in comparison with $pp$ collisions at $\sqrt{s}=5.02~\mathrm{TeV}$. The Pb+Pb data, collected in 2018, have an integrated luminosity of $1.72~\mathrm{nb^{-1}}$, while the $pp$ data, collected in 2017, have an integrated luminosity of $260~\mathrm{pb}^{-1}$. Jets used in this analysis are clustered using the anti-$k_{t}$ algorithm with a radius parameter $R=0.4$. The jet constituents, defined by both tracking and calorimeter information, are used to determine the angular scale $r_\mathrm{g}$ of the first hard splitting inside the jet by reclustering them using the Cambridge-Aachen algorithm and employing the soft-drop grooming technique. The nuclear modification factor, $R_\mathrm{AA}$, used to characterize jet suppression in Pb+Pb collisions, is presented differentially in $r_\mathrm{g}$, jet transverse momentum, and in intervals of collision centrality. The $R_\mathrm{AA}$ value is observed to depend significantly on jet $r_\mathrm{g}$. Jets produced with the largest measured $r_\mathrm{g}$ are found to be twice as suppressed as those with the smallest $r_\mathrm{g}$ in central Pb+Pb collisions. The $R_\mathrm{AA}$ values do not exhibit a strong variation with jet $p_\mathrm{T}$ in any of the $r_\mathrm{g}$ intervals. The $r_\mathrm{g}$ and $p_\mathrm{T}$ dependence of jet $R_\mathrm{AA}$ is qualitatively consistent with a picture of jet quenching arising from coherence and provides the most direct evidence in support of this approach.