KODIAQ-Z: Metals and Baryons in the Cool Intergalactic and Circumgalactic Gas at 2.2 less than or similar to z less than or similar to 3.6

We present the KODIAQ-Z survey aimed to characterize the cool, photoionized gas at 2.2 less than or similar to z less than or similar to 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 less than or similar to z less than or similar to 3.6 can be metal-rich (-1.6 less than or similar to [X/H] less than or similar to - 0.2) as seen in damped Ly alpha 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 Delta nu < 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 less than or similar to z less than or similar to 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 similar to 8 from 2.2 less than or similar to z less than or similar to 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 less than or similar to z less than or similar to 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 similar to 2-3 are tracers of inflows, while higher-metallicity absorbers are a mixture of inflows and outflows.