Fuel pressure mystery

Where are you measuring the fuel pressure?
Before or After the Mechanical Pump?
Is your boost pump a rotary or solenoid type?
What drain hose?
Does the fuel pressure vary with airspeed?  Stall vs. Power On/Off Dive?
Does the fuel pressure vary with Power?  Idle vs. Wide open?

This sounds like a measurement problem, not a fuel flow problem.
The carbs need enough flow to keep the bowls full.
This is the ultimate goal.
Any excess flow capacity will be blocked by the float valve.
The fuel pressure is an Indicator, not a measure, of flow capacity.
1 psi or possibly less can often be sufficient, but 3-5-7psi produces a generous safety margin, especially in a nose-high climb.

Not sure if its relevant but there was a small amount of engine oil in the-fuel pump drain bottle - may be 2-5 ml

Sensor after mechanical pump - pipe from fuel distributer, sensor of firewall.

Drain hose on mechanical pump

Don't know the unswear to next two airspeed and engine speed.

This has been a mystery for many years with the 912uls; there are many old threads dealing with this subject. In most of the cases the pressure falls off during climbout (but not always) and usually recovers after a while at level cruise. In the majority of cases the engine maintains full power and never hiccups even during the low pressure time. It happened to me many, many times thru a 9 year period from new to about 1000 hours. I finally quit worrying about it because it never once caused a problem, and I do not have a backup fuel pump. I fly a high wing Kitfox. No one has ever had a reasonable explanation for it and it remains a mystery to me to this day. My own suspicion is that it has something to do with the fuel pump (newer version) rather than a sensor problem, which has been double checked many times by many people.

I will admit your problem could be different because you say that after the low readings you must keep the backup pump on for the rest of the flight. Most of the rest of us found the pressure recovers by itself after a short while. You might try leaving your backup pump off for a while and see what happens.

Seems like lots of low wings have this issue, but not high wings. Vans RV12 and Sting aircraft see to have this issue. Even though the pressure drops I haven't heard of any engine issues. It may be a fuel pressure sensor issue. I do know the the engine will run lower than the 2.2 psi that is the Rotax minimum. I did a research project on this once.

Kitfox IV with 912UL with 921 hours with rebuild at 898 hours.

The following does not provide any solutions, just my experiences with this engine.

I have a piece of clear poly in the fuel pump vent line that creates a trap as it is routed over the engine to vent at the bottom of the firewall. I always have some thin black fluid in that line that moves back and forth as the prop is rotated. I replaced the pump thinking that may be an indication of seal failure but the new pump immediately did the same.

Recently, I started collected each vent line(fuel pump, oil tank and carb vents) into its own test tube to see how much venting of fluids was going on. Nothing collected in the fuel pump vent test tube, some condensation collected in the oil tank vent test tub and the right carb vent tube collected about 1/2 ounce of fuel.

I have always been curious about the fuel pump vent output as I thought any venting would be a sign of seal failure. Any thoughts?

I have an inline fuel pressure regulator due to being unable to stop the carbs from massive fuel venting after rebuilding and balancing multiple times. Anything above 4psi will lead to fuel overboard so I run the regulator at 3.5psi. During takeoff the pressure will drop to 2.2 psi.