Does the critical density of the Universe also include Dark Energy? It is often said that it seems that the Universe is quite close to critical density (for example https://astronomy.swin.edu.au/cosmos/C/Critical+Density).
Does this include Dark Energy as well (apart from Dark matter and Baryonic matter)?
Yes. Quoting values from wikipedia (which in turn cites Ade et.al. in Astronomy and Astrophyics 517), the contribution of matter (both Dark and visible matter) is
$$Ω_\text{mass} ≈ 0.315±0.018$$
The contribution of photons and neutrinos is small, and within the boundaries of error of the other terms:
$$Ω_\text{relativistic} ≈ 9.24×10^{−5}$$
And the contribution of Dark Energy is:
$$Ω_Λ ≈ 0.6817±0.0018$$
$$Ω_\text{total}= Ω_\text{mass} + Ω_\text{relativistic} + Ω_Λ= 1.00±0.02$$