  We present a determination of the ratio of kaon and pion leptonic decay
constants in isosymmetric QCD (isoQCD), $f_K / f_\pi$, making use of the gauge
ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f
= 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, including
configurations close to the physical point for all dynamical flavors. The
simulations are carried out at three values of the lattice spacing ranging from
$\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm.
The scale is set by the PDG value of the pion decay constant, $f_\pi^{isoQCD} =
130.4~(2)$ MeV, at the isoQCD pion point, $M_\pi^{isoQCD} = 135.0~(2)$ MeV,
obtaining for the gradient-flow (GF) scales the values $w_0 = 0.17383~(63)$ fm,
$\sqrt{t_0} = 0.14436~(61)$ fm and $t_0 / w_0 = 0.11969~(62)$ fm. The data are
analyzed within the framework of SU(2) Chiral Perturbation Theory (ChPT)
without resorting to the use of renormalized quark masses. At the isoQCD kaon
point $M_K^{isoQCD} = 494.2~(4)$ MeV we get $(f_K / f_\pi)^{isoQCD} =
1.1995~(44)$, where the error includes both statistical and systematic
uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa (CKM) matrix
element $|V_{us}|$ and for the first-row CKM unitarity are discussed.
