The ATLAS detector at the Large Hadron Collider has been used to measure jet substructure modification and suppression in $\mathrm{Pb}+\mathrm{Pb}$ collisions at a nucleon--nucleon center-of-mass energy $\sqrt{{s}_{{}_{NN}}}=5.02\phantom{\rule{0.16em}{0ex}}\mathrm{TeV}$ in comparison with proton--proton ($pp$) collisions at $\sqrt{s}=5.02\phantom{\rule{0.16em}{0ex}}\mathrm{TeV}$. The $\mathrm{Pb}+\mathrm{Pb}$ data, collected in 2018, have an integrated luminosity of $1.72\phantom{\rule{0.16em}{0ex}}{\mathrm{nb}}^{\ensuremath{-}1}$, while the $pp$ data, collected in 2017, have an integrated luminosity of $260\phantom{\rule{0.16em}{0ex}}{\mathrm{pb}}^{\ensuremath{-}1}$. 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, ${R}_{AA}$, used to characterize jet suppression in $\mathrm{Pb}+\mathrm{Pb}$ collisions, is presented differentially in ${r}_{\mathrm{g}}$, jet transverse momentum, and in intervals of collision centrality. The ${R}_{AA}$ 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 $\mathrm{Pb}+\mathrm{Pb}$ collisions. The ${R}_{AA}$ 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 ${R}_{AA}$ is qualitatively consistent with a picture of jet quenching arising from coherence and provides the most direct evidence in support of this approach.