  Layered van der Waals magnets have attracted much recent attention as a
promising and versatile platform for exploring intrinsic two-dimensional
magnetism. Within this broader class, the transition metal phosphorous
trichalcogenides $M$P$X_3$ stand out as particularly interesting, as they
provide a realization of honeycomb lattice magnetism and are known to display a
variety of magnetic ordering phenomena as well as superconductivity under
pressure. One example, found in a number of different materials, is
commensurate single-$Q$ zigzag antiferromagnetic order, which spontaneously
breaks the spatial threefold $(C_3)$ rotation symmetry of the honeycomb
lattice. The breaking of multiple distinct symmetries in the magnetic phase
suggests the possibility of a sequence of distinct transitions as a function of
temperature, and a resulting intermediate $\mathbb{Z}_3$-nematic phase which
exists as a paramagnetic vestige of zigzag magnetic order -- a scenario known
as vestigial ordering. Here, we report the observation of key signatures of
vestigial Potts-nematic order in rhombohedral FePSe$_3$. By performing linear
dichroism imaging measurements -- an ideal probe of rotational symmetry
breaking -- we find that the $C_3$ symmetry is already broken above the N\'eel
temperature. We show that these observations are explained by a general
Ginzburg-Landau model of vestigial nematic order driven by magnetic
fluctuations and coupled to residual strain. An analysis of the domain
structure as temperature is lowered and a comparison with zigzag-ordered
monoclinic FePS$_3$ reveals a broader applicability of the Ginzburg-Landau
model in the presence of external strain, and firmly establishes the $M$P$X_3$
magnets as a new experimental venue for studying the interplay between
Potts-nematicity, magnetism and superconductivity.
