Cars have many computers these days. Transmission fault codes are generally stored in a different computer than the engine codes.
Automatic transmissions (even CVT’s) are sort of a hydraulic-controlled computer. Fluid pressure places a force on an actuator, which causes something to move to effect the shift operation. The valve body has complicated looking arrangement of channels for the fluid to flow through, and valves which direct it in the desired path. If the valves stick or the seals leak, it won’t allow the high pressures to build up needed to create the large forces to cause the shifting operation. Newer automatics like yours use some electrical-operated solenoid valve, screw into valve body, sometimes the problem is just one of those has failed. There are other hydraulic valves, and generally only replaced during transmission overhaul/rebuild.
The CEL is for emissions related issues and uses the OBD-II (On Board Diagnostics) system. Transmission codes are not emissions related and are still stored. A sophisticated scanner can read the transmission codes as well as the OBD-II codes. It looks like you are on your way to a successful repair. If they have the parts, it should be a quick repair. If they have to order them you have the loaner at least. Good luck.
A friend owned a Ford Focus with the 6 speed DDCT. This was a very problematic model and was experiencing a lot of problems. His car got a new transmission about every 30,000 miles and he said he drove it like an old woman to try and avoid problems. The original warranty was much less but various class action suits extended the warranty on his car several times in regards to the transmission. I bet this is the case here as the Nissan CVTs were not known for reliability. In his case, the car got another new transmission about 10K before the warranty finally expired. Once he reached the end of the warranty, he sold that car while the transmission was still good.