Cigarette lighter and auxiliary socket not working?

Could you tell me which fuse you are replacing? The info I have shows a master APO/RAP 50 amp fuse that feeds into a 15 amp circuit breaker not a fuse for each of the outlets.

Does the fuse blow in both outlets or only one? Have you tried a different item like a light or similar to see if anything else will blow the fuse. If those do as well then I suspect the issue is in the wiring behind the console. I would first verify that nothing is in the power port like a penny or similar that could short it out. If there is nothing then take something plastic like a Bic pen or even a popsicle stick and press the center contact gently to see if the fuse blows. If it does then the console needs to be removed to access the wiring and repair it. Not a real hard job if you are handy with tools. The first three pictures show prying up the top trim using a plastic trim tool. Next you use the tool to remove the side trim plates from the console. The drivers side has a hook that must be disengaged to remove it, the passenger side just pries off to release the clips. Then the console itself unbolts as shown in the last picture. That gives you access to the wiring.

HMM, that is the 110 volt inverter plug not a 12 volt outlet. Most of the above no longer applies. Your description however points to a failed inverter module. The inverter is normally off. When you plug something into it the unit turns on. The fuse blows at that time because of a fault in the inverter. Replacing the module isn't that hard, easier than the above really. You remove the knee bolster from under the drivers side dash panel by removing the screws, Then remove the drivers side duct extension by removing the plastic push pin and sliding it off. Next you remove the wire connections from the module and the retainer nut from the bracket and the inverter slides off the upper pin and out. Reverse the process to install the replacement module. If the info is correct it is a GM #84181077

As for the wireless charger, it is sort of touchy in what it works with. However a dealer should have an inductive tester that slips into the slot and tests if the unit is operating. That test item is the only way I know of to test that module.

You do have a fuse for the aux outlets which would be what these are called. You need to look at fuse 41 and make sure that is okay. Let us know if there is more info needed. Thanks

https://www.2carpros.com/articles/how-to-check-a-car-fuse