A metal is reflective because it is conductive. Conductivity will limit reflectivity as it gets thin and narrow.
There are considerations beyond this of course if you want to make a solar sail. A metal wire mesh as thin as possible would be weak and fragile. Strength matters. Manufacturability of giant a sail matters. Ability to survive Earth's atmosphere before launch, launch, and deployment matter. Radiation damage matters. But I will focus on things that affect reflectivity.
Choice of material matters. One problem with gold is its reflectivity across the spectrum. You want it most reflective at wavelengths the Sun emits more strongly. This is the spectrum.
This is the reflectivity.
Gold is less reflective (less conductive) than silver or aluminum across an important part of the spectrum.
Reflection happens at the surface of a metal. Radiation makes conduction electrons vibrate. Vibrating electrons radiate. This is is the reflected light. The current decays exponentially with depth into the metal. The decay constant is depends on conductivity.
$$J = J_s e^{-(1+j)d/ \sigma}$$
where $\sigma$ is the skin depth
$$\sigma = \sqrt{\frac{2 \rho}{\omega \mu}}$$
If the layer of gold is thinner than a few $\sigma$, light will be transmitted though it. For gold, this is fairly thick. As the link in the post says, a $500$ angstrom layer of gold on astronaut's faceplates reflected essentially all of the infrared, but about half the visible. This is what you want for a faceplate more than a solar sail.
On the other hand, your link How realistic is the 1 kg/km² solar sail in “Death's End”? says that a 5 nm Al "foil" is optimal. At that thickness, Al is $50$% reflective. Then it suggests a grid of $5$ nm wires would also be effective.
The link is interested in getting the weight down as much as reflectivity up. It was not mentioned, but perhaps a grid of say $10$ nm wires would be closer to $100$% reflective, and not that heavy. A wire grid would be strengthened with other stronger wires.
Another consideration is that a metal is reflective because electrons spread out through the metal. They can easily move, which makes them conductive. Classically, the oscillating electric field in light vibrates the electrons, and vibrating electrons radiate light. It works out that the incoming light is absorbed and the radiated light is the reflection.
Electrons can move because neighboring atoms don't have individual separate orbitals, each with the same energy. Instead, they overlap and forming bands, states with many closely spaced energy levels.
Gold is such a solid. Gold is more conductive at lower frequencies. Red and infrared light is reflected well, but blue light is absorbed. So gold is gold colored.
For this to work, there have to be enough metal atoms to make a solid with a band structure. The solid must be big enough for the electrons to vibrate and radiate.
The thinnest sputtered gold films are typically $10$ nm thick. Below that, gold forms islands rather than a film. This paper gets it down to $5.4$ nm and seems to say that the optical properties are comparable to what you would expect in bulk gold. There is an effect from the substrate, but in a solar sail, people are talking about (perhaps wishing for) removable substrates. Still, it might be difficult to make gold wires this thin.
Given that a $54$ angstrom film behaves like bulk, skin depth is the limiting factor in a film.
It is hard to make wires as thin and narrow as a film. Sample records for thin gold wires has some links. One, Gold Wire-networks: Particle Array Guided Evaporation Lithograpy, is an abstract that mentions hopes to deposit wires in the micron to submicron range. I could not find the paper itself.
Wires must run in multiple directions. Light polarized parallel to the wires can excite electrons to vibrate along the length of the wire, and is reflected well. Light polarized perpendicular to the wires cannot, and is not reflected.
Wires must be spaced less than a wavelength of light apart or light will diffract between them.
