The expression $$d=zc/H$$ is a nonrelativistic approximation, valid in the limit that $z\ll 1$ and correspondingly the recession velocity $Hd\simeq zc\ll c$. In this low-velocity regime, relativistic effects like Lorentz contraction and the relativity of simultaneity are negligible, so there is no ambiguity about the distance.

For a FLRW cosmology (that is, a homogeneous universe) with Hubble rate $H(z)$, The full expression is $$d=c\int_0^z \frac{\mathrm{d}z'}{H(z')}.$$ Assuming that the observed object is comoving with the Hubble flow, $d$ is the distance to that object's worldline measured along the comoving synchronous spatial surface, which is the 3D surface (in 4D spacetime) on which all observers who are comoving with the Hubble flow agree on the time elapsed since the beginning of the universe. In particular, all observers agree on the definition of these surfaces, so all observers agree on the distance $d$.

The expression $$d=zc/H$$ is a nonrelativistic approximation, valid in the limit that $z\ll 1$ and correspondingly the recession speed $Hd\simeq zc\ll c$. In this low-velocity regime, relativistic effects like Lorentz contraction and the relativity of simultaneity are negligible, so there is no ambiguity about the distance.

For a FLRW cosmology (that is, a homogeneous universe) with Hubble rate $H(z)$, The full expression is $$d=c\int_0^z \frac{\mathrm{d}z'}{H(z')}.$$ Assuming that the observed object is comoving with the Hubble flow, $d$ is the distance to that object's worldline measured along the comoving synchronous spatial surface, which is the 3D surface (in 4D spacetime) on which all observers who are comoving with the Hubble flow agree on the time elapsed since the beginning of the universe. In particular, all observers agree on the definition of these surfaces, so all observers agree on the distance $d$.

The expression $$d=zc/H$$ is a nonrelativistic approximation, valid in the limit that $z\ll 1$ and correspondingly the recession velocity $Hd\simeq zc\ll c$. In this low-velocity regime, Lorentz contraction is negligible, so there is no ambiguity about the distance.

For a FLRW cosmology (that is, a homogeneous universe) with Hubble rate $H(z)$, The full expression is $$d=c\int_0^z \frac{\mathrm{d}z'}{H(z')}.$$ Assuming that the observed object is comoving with the Hubble flow, $d$ is the distance to that object's worldline measured along the comoving synchronous spatial surface, which is the 3D surface (in 4D spacetime) on which all observers who are comoving with the Hubble flow agree on the age of the universe. In particular, all observers agree on the definition of these surfaces, so all observers agree on the distance $d$.

The expression $$d=zc/H$$ is a nonrelativistic approximation, valid in the limit that $z\ll 1$ and correspondingly the recession velocity $Hd\simeq zc\ll c$. In this low-velocity regime, relativistic effects like Lorentz contraction and the relativity of simultaneity are negligible, so there is no ambiguity about the distance.

For a FLRW cosmology (that is, a homogeneous universe) with Hubble rate $H(z)$, The full expression is $$d=c\int_0^z \frac{\mathrm{d}z'}{H(z')}.$$ Assuming that the observed object is comoving with the Hubble flow, $d$ is the distance to that object's worldline measured along the comoving synchronous spatial surface, which is the 3D surface (in 4D spacetime) on which all observers who are comoving with the Hubble flow agree on the time elapsed since the beginning of the universe. In particular, all observers agree on the definition of these surfaces, so all observers agree on the distance $d$.