  Lattice strains of appropriate symmetry have served as an excellent tool to
explore the interaction of superconductivity in the iron-based superconductors
with nematic and stripe spin-density wave (SSDW) order, which are both closely
tied to an orthorhombic distortion. In this work, we contribute to a broader
understanding of the coupling of strain to superconductivity and competing
normal-state orders by studying CaKFe$_4$As$_4$ under large, in-plane strains
of $B_{1g}$ and $B_{2g}$ symmetry. In contrast to the majority of iron-based
superconductors, pure CaKFe$_4$As$_4$ exhibits superconductivity with
relatively high transition temperature of $T_c\,\sim\,$35 K in proximity of a
non-collinear, tetragonal, hedgehog spin-vortex crystal (SVC) order. Through
experiments, we demonstrate an anisotropic in-plane strain response of $T_c$,
which is reminiscent of the behavior of other pnictides with nematicity.
However, our calculations suggest that in CaKFe$_4$As$_4$, this anisotropic
response correlates with the one of the SVC fluctuations, highlighting the
close interrelation of magnetism and high-$T_c$ superconductivity. By
suggesting moderate $B_{2g}$ strains as an effective parameter to change the
stability of SVC and SSDW, we outline a pathway to a unified phase diagram of
iron-based superconductivity.
