The photo the OP posted is a little confusing as it does show the TRD Pro interior (black trim and then the shift knob) with the limited AC cluster, unless something was changed for 2016 this is not a possible combo.
Anyways onto the more interesting stuff.
Someone on here already tried a direct swap of JUST the auto climate control cluster and IIRC it will plug in however it does not control so you would loose AC/Heat but you would have your digital readout. I did a decent amount of digging in the FMS and parts diagrams and I think it can be done but the cost is prohibitive unless you really want it or you can find a salvaged/junkyard 5th gen. Parts I think you need. I got a dealer quote for the servos and control unit and i think it was around $1700-1800
*Auto Climate Control control Pane
*Wiring harness (for the Auto panel) - maybe not needed
* 3 blend servos for the aC "climate box" under the dash
if anyone has a limited in the Twin Cities area and would be willing to dig into the dash with me (or let me) I would LOVE to see if this is indeed a direct swap. I really miss the auto climate control (hell my wife's 02 Lexus has it). I even contemplating finding a rental place that had a limited and doing a temporary swap to see if it functions as expected but couldn't find a limited (all SR5's).