  We present an update of our determination of the isovector charges
$g_A^{u-d}$, $g_S^{u-d}$ and $g_T^{u-d}$, and the isovector twist-2 forward
matrix elements $\langle x\rangle_{u-d}$, $\langle x\rangle_{\Delta u-\Delta
d}$ and $\langle x\rangle_{\delta u-\delta d}$ on the $N_\mathrm{f}=2+1$ gauge
ensembles generated by the Coordinated Lattice Simulations (CLS) effort. We
have significantly extended our coverage of the parameter space by adding
ensembles at the physical pion mass and fine lattice spacing, at
nearly-physical pion masses and very fine lattice spacings, and at very large
physical lattice volumes, enabling a well-controlled extrapolation to the
physical point. Another major improvement is achieved owing to the extended
range of source-sink separations, which allows us to perform two-state fits to
summed correlator ratios, leading to a much higher level of control over
excited-state effects. Systematic uncertainties from the chiral, continuum and
infinite-volume extrapolations are incorporated via model averages based on the
Akaike Information Criterion. Our final results at the physical point are
$g_A^{u-d} = 1.254(19)_\mathrm{stat}(15)_\mathrm{sys}[24]_\mathrm{total}$,
$g_S^{u-d} = 1.203(77)_\mathrm{stat}(81)_\mathrm{sys}[112]_\mathrm{total}$,
$g_T^{u-d} = 0.993(15)_\mathrm{stat}(05)_\mathrm{sys}[16]_\mathrm{total}$,
$\langle x\rangle_{u-d} =
0.153(15)_\mathrm{stat}(10)_\mathrm{sys}[17]_\mathrm{total}$, $\langle
x\rangle_{\Delta u - \Delta d} =
0.207(15)_\mathrm{stat}(06)_\mathrm{sys}[16]_\mathrm{total}$, and $\langle
x\rangle_{\delta u - \delta d} =
0.195(17)_\mathrm{stat}(15)_\mathrm{sys}[23]_\mathrm{total}$. While our results
for the isovector charges are in excellent agreement with the FLAG\,21
averages, we note that our error for the tensor charge $g_T^{u-d}$ is
considerably smaller.
