  We report the thermodynamic properties studied by thermal expansion,
magnetostriction, magnetisation, and specific heat measurements as well as the
low-energy magnetic excitations of \mto\ and investigate how magneto-elastic
coupling and magnetic anisotropy affect the evolution of long-range order and
the magnetic phase diagram. Specifically, we utilise high-resolution
capacitance dilatometry and antiferromagnetic resonance (AFMR) studies by means
of high-frequency electron spin resonance (HF-ESR) spectroscopy. The role of
anisotropy is reflected by spin-reorientation at $B_{\rm{SF}}$~$\simeq 6$~T and
a corresponding sign change in $\partial T_{\rm N}/\partial B$. Analysis of the
AFMR modes enables us to establish the zero-field excitation gap $\Delta$ as
well as its temperature dependence. We derive the effective anisotropy field
$B_\mathrm{A} = 0.16(1)$~T which predominately originates from out-of-plane
nearest-neighbour dipole-dipole interactions. Despite the nearly fully quenched
orbital moment, our data show pronounced thermal expansion and magnetostriction
anomalies at $T_{\rm N}$ and $B_{\rm{SF}}$ , respectively, which allows the
experimental determination of sizable uniaxial pressure dependencies, i.e.,
$\partial B_{\rm SF}/\partial p_{\rm c} = -0.20(2)$~T/GPa, $\partial T_{\rm N}/
\partial p_b = 0.69(12)$~K/GPa, and $\partial T_{\rm N}/ \partial p_c =
-2.0(4)$~K/GPa. Notably, short-range magnetic order appears up to at least
3$T_{\rm N}$ , as indicated by anisotropic lattice distortion, the violation of
a constant Gr\"uneisen behavior, and the presence of local magnetic fields
detected by HF-ESR.
