Yeah, 13 mpg isn't surprising for that 2011 Z71, especially if a lot of that 40 mins was idling or stop-and-go driving. Actually, GM's Vortec 5.3L engines from that era are known for burning through fuel pretty fast under certain conditions. The Active Fuel Management (AFM) system, which was supposed to improve mileage by shutting down cylinders, can be hit or miss. If yours is still running AFM, it might be deactivating less efficiently due to age or carbon buildup ... common issue with these engines.
Might wanna check for things like a dirty MAF sensor, weak O2 sensors, or even low tire pressure ...all of those can quietly drag your mpg down. Silverado tanks are big too, so losing half a tank might just feel worse than it actually is.