Hi and welcome to AirForums. These vintage Airstreams are a lot of fun and frustration. My hobby is a 66 Trade Wind, one size up from your Safari.
Why no city water pressure when you hook it up? You'll have to see where the water is going. Your water system is designed to pressurize a faucet EITHER from the 12v
pump and fresh water tank, OR from city water hook up. There is likely a water pressure reducing valve close to where you hook city water up. Maybe it's full of debris. There may be a water filter plugged up blocking flow. There is likely a check valve preventing your 12v
pump from spraying water out the city water connection hose. Old trailers sometimes have "fresh water fill valve" that allows filling the fresh water tank from the city water pressure. Maybe the city water is simply filling your fresh water tank and not giving you any pressure.
You will soon learn the fun of diagnosing a problem and solving it yourself. I find Air Forum members are more than willing to help find the cause of the problem.