  The kagome materials AV4$_3$Sb$_5$ (A = K, Rb, Cs) host an intriguing
interplay between unconventional superconductivity and charge-density-waves.
Here, we investigate CsV$_3$Sb$_5$ by combining high-resolution
thermal-expansion, heat-capacity and electrical resistance under strain
measurements. We directly unveil that the superconducting and charge-ordered
states strongly compete, and that this competition is dramatically influenced
by tuning the crystallographic c-axis. In addition, we report the absence of
additional bulk phase transitions within the charge-ordered state, notably
associated with rotational symmetry-breaking within the kagome planes. This
suggests that any breaking of the C$_6$ invariance occurs via different
stacking of C$_6$-symmetric kagome patterns. Finally, we find that the
charge-density-wave phase exhibits an enhanced A$_{1g}$-symmetric
elastoresistance coefficient, whose large increase at low temperature is driven
by electronic degrees of freedom.
