I think you need to do a little research on your RV and maybe a belated pre-delivery instructional tour of your units operations.
The tanks are probably fresh water, grey water (sink and shower) and black tank for the toilet.
To prime most pumps if they need it then I suggest you find the pump. Mine was behind a panel that was screwed shut rather than having a door to get to it. My inside drain valves and the valves to divert water from getting into the hot water heater were all located near it. I added self closing hinges to this panel so I could access it more easily.
Attached to my pump was a 3 foot piece of flexible plastic hose with a valve near the pump. To winterize, I and most others take a gallon jug (s) of pink, non-toxic antifreeze and use the pump and the little hose to suck it up and push it through the lines to the sink, shower, toilet, etc.
Hopefully this will help you figure out what you need to do. It may be the pump filter is blocked, the valves are set wrong, the pipe to the tank is bad or the pump is bad. If the motor runs but the pump won't work some can be rebuilt.
Use the search function above and you find a lot of posts on pump problems. Good luck!
2017 SLX 195RB
2021 Jeep Grand Cherokee Summit L 5.7L V8
Andersen WDH hitch, Renogy 100 AH Lithium &
200 Watts solar panels from Renogy
Prev. '14 Jeep Grand Cherokee Overland, gas 3.6 V6