We present the KODIAQ-Z survey aimed to characterize the cool, photoionized gas at 2.2 ≲ z ≲ 3.6 in 202 H i-selected absorbers with 14.6 ≤
log
N
H
I
< 20 that probe the interface between galaxies and the intergalactic medium (IGM). We find that gas with
14.6
≤
log
N
H
I
<
20
at 2.2 ≲ z ≲ 3.6 can be metal-rich (−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 ([X/H] < − 3.8), which is not observed in DLAs but is common 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%) at these redshifts. 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 Δv < 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 14% of the cosmic baryons and 45% of the cosmic metals at 2.2 ≲ z ≲ 3.6. We find that 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 a quarter of that at 2.2 ≲ z ≲ 3.6. We show that FOGGIE cosmological zoom-in simulations have a similar evolution of [X/H] with N
H i
, which is not observed in lower-resolution simulations. In these simulations, very metal-poor absorbers with [X/H] < − 2.4 at z ∼ 2–3 are tracers of inflows, while higher-metallicity absorbers are a mixture of inflows and outflows.