We present the KODIAQ-Z survey aimed to characterize the cool, photoionized gas at 2.2 z 3.6 in 202 H Iselected absorbers with 14.6 ≤ log N H I < 20, i.e., the gaseous interface between galaxies and the intergalactic medium (IGM). We find that the 14.6 ≤ log N H I < 20 gas at 2.2 z 3.6 can be metal-rich gas (−1.6 [X/H] −0.2) as seen in damped Lyα absorbers (DLAs); it can also be very metal-poor ([X/H] < −2.4) or even pristine gas ([X/H] < −3.8) not observed in DLAs, but commonly observed in the IGM. For 16 < log N H I < 20 absorbers, the frequency of pristine absorbers is about 1%-10%, while for 14.6 ≤ log N H I ≤ 16 absorbers it is 10%-20%, similar to the diffuse IGM. Supersolar gas is extremely rare (< 1%) in this gas. The factor of several thousand spread from the lowest to highest metallicities and large metallicity variations (a factor of a few to > 100) between absorbers separated by less than ∆v < 500 km s −1 imply that the metals are poorly mixed in 14.6 ≤ log N H I < 20 gas. We show that these photoionized absorbers contribute to about 10% of the cosmic baryons and 30% of the cosmic metals at 2.2 z 3.6. We find the mean metallicity increases with N H I , consistent with what is found in z < 1 gas. The metallicity of gas in this column density regime has increased by a factor ∼8 from 2.2 z 3.6 to z < 1, but the contribution of the 14.6 ≤ log N H I < 19 absorbers to the total metal budget of the universe at z < 1 is half that at 2.2 z 3.6, indicating a substantial shift in the reservoirs of metals between these two epochs. We compare the KODIAQ-Z results to FOGGIE cosmological zoom simulations. The simulations show an evolution of [X/H] with N H I similar to our observational results. Very metal-poor absorbers with [X/H] < −2.4 at z ∼ 2-3 in these simulations are excellent tracers of inflows, while higher metallicity absorbers are a mixture of inflows and outflows.