A search is presented for charged, long-lived supersymmetric particles in final states with one or more disappearing tracks. The search is based on data from proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the CERN LHC between 2016 and 2018, corresponding to an integrated luminosity of $137{\mathrm{fb}}^{-1}$. The search is performed over final states characterized by varying numbers of jets, $b$-tagged jets, electrons, and muons. The length of signal-candidate tracks in the plane perpendicular to the beam axis is used to characterize the lifetimes of wino- and Higgsino-like charginos produced in the context of the minimal supersymmetric standard model. The $dE/dx$ energy loss of signal-candidate tracks is used to increase the sensitivity to charginos with a large mass and thus a small Lorentz boost. The observed results are found to be statistically consistent with the background-only hypothesis. Limits on the pair-production cross section of gluinos and squarks are presented in the framework of simplified models of supersymmetric particle production and decay, and for electroweakino production based on models of wino and Higgsino dark matter. The limits presented are the most stringent to date for scenarios with light third-generation squarks and a wino- or Higgsino-like dark matter candidate capable of explaining the observed dark matter relic density.