Does Smeaton's coefficient have a modern accepted value or it is dependent of the air density?
There is no modern equivalent to the Smeaton coefficient, therefore it has no "modern" value.

The Smeaton coefficient is supposed to represent a "coefficient of air pressure" (and thus indirectly density), but it is a false constant: There is no single value because air pressure is not a constant value, but rather a variable (depending on altitude, temperature, etc.).

As you noted lift is calculated by a different formula today, using actual density of the fluid (air) you're moving through in place of the Smeaton coefficient.

$ L = Cl \cdot \frac{(A \cdot \rho)}{2} \cdot V^2$

You can calculate the Smeaton coefficient at any given location/altitude with simple algebra if you know the air density: Solve the modern lift equation, plug the values into the "old" Wright Brothers era equation, and solve for $k$.

The density-based calculation also has the benefit of working in other fluids besides air. (The same equation can give you hydrodynamic lift for boats and submarines by plugging in the density of water - itself a dynamic value depending on temperature, salinity, etc.)