All of this probably seems really confusing. Most water heaters do have bypass valves that are commonly used for winterizing. Many water heaters are installed in locations that make them hard or impossible to get to as they are usually on the back side of the water heater. Mine can theoretically be reached by pulling drawers out of a dresser and contorting yourself while stretching beyond the limits of human arm length. Many people, including me, never use them. Also, many (most) RVs don't come with plumbing diagrams and many don't really provide any help with locating valves, tanks, etc.
So you may or may not need to find these bypass valves. What others have said regarding operating the heater with an empty tank is very important though. Nothing good comes from operating the water heater with an empty tank. In propane mode, it MAY not hurt anything, but in electric mode, as others have already suggested, it will quickly burn out the heating element.
So how do you verify the tank is full of water? This is where someone was suggesting to you to use the over pressure (OTP) valve. If the water system is under pressure, either from the "city water" inlet or water in the tank with the water pump on, and you pull the manual release on the over pressure valve, it will allow you determine if the tank is full. While the tank is filling with water, you should feel and hear air coming out of the opened valve. Once the tank is full or near full, water should start to flow from it. If the water has been on for a while and you don't see/hear air and water from the OTP valve when its open, then your heater has likely been bypassed and you will need to find the bypass valves to restore water flow.
Once you've verified that the tank is full, then turn on the heater and verify that it is heating as expected. You can run it in electric only, propane only, or both.