Sounds to me like your power steering pump has gone bad. Being a vehicle with a hydro-boost brake system that would explain the simultaneous power brake failure. Hydro-boost brake systems utilize pressurized power steering fluid to provide brake assist. In most lighter GVWR vehicles this function is performed by engine vacuum. There is a recall on certain Silverados and Sierras that addresses a faulty check ball in the booster, but your vehicle is affected by a steering issue as well. This would indicate to me that it is the pump. You can however check online to verify if your vehicle is affected by the recall. Go to the Edmunds.com webpage and click on “tips and advice” button. Then click on the car maintenance button. Here is the specific site:
Enter your year make and model and the mileage and your zip code. This section will list all the TSBs and recalls on your vehicle. Good luck!