  We carry out a systematic study of the effective bosonic string describing
confining flux tubes in $\mathrm{SU}(N)$ Yang--Mills theories in three
spacetime dimensions. While their low-energy properties are known to be
universal and are described well by the Nambu--Got\=o action, a non-trivial
dependence on the gauge group is encoded in a series of undetermined subleading
corrections in an expansion around the limit of an arbitrarily long string. We
quantify the first two of these corrections by means of high-precision Monte
Carlo simulations of Polyakov-loop correlators in the lattice regularization.
We compare the results of novel lattice simulations for theories with $N=3$ and
$6$ color charges, and report an improved estimate for the $N=2$ case,
discussing the approach to the large-$N$ limit. Our results are compatible with
analytical bounds derived from the S-matrix bootstrap approach. In addition, we
also present a new test of the Svetitsky--Yaffe conjecture for the
$\mathrm{SU}(3)$ theory in three dimensions, finding that the lattice results
for the Polyakov-loop correlation function are in excellent agreement with the
predictions of the Svetitsky--Yaffe mapping, which are worked out
quantitatively applying conformal perturbation theory to the three-state Potts
model in two dimensions. The implications of these results are discussed.
