It's more that just pressure, you need volume. A weak pump bypasses internally making just enough volume to run the engine but not much more so little fuel bypasses the regulator and heads back to the tank.

Replacing the senders won't fix your fuel transfer problem. My 97 C280 was siting 4 + years before I got it and the sender wipers were corroded. They can be taken apart and wiper cleaned. The resistor is thick film so don't scrub it too hard and damage the resistive surface.

Also, the senders are wired in series to give proper fuel level and there isn't any sort of monitoring done to transfer fuel.

A filling issue may be a collapsed vent hose near the filler, if this has roll over check valves that might cause a problem as well.