repeatedly getting air into baseboard hot water - need to find root cause

A properly-functioning hot water system should never be refilling.

This boiler design likely includes a pressure sensor that will fault off the boiler if the pressure drops below 10 psi. If air is entering the system it is likely coming from the fill water source. If on well water there could be dissolved gasses (CO2) that are released from the water as it sets there in the home. If the fill line comes off the top of a domestic line it is likely collecting this air slowly over time until the system calls for additional make up fluid. The zone with the black pump seems to be the one that collects the air? I question if the spiro vent is working as it should. Ultimately you may have a system leak somewhere. If not a leak from the home side of the system, try capturing any condensate from the boiler to see if it might continue when the boiler is not in use. I've had to replace a boiler section on this style due to a sand hole in the casting that showed up several years post installation and was not discovered until it was noticed that the condensate water had an antifreeze color to it.

pretty sure they said it is off a couple posts ago…

losing tiny amount of water isn't abnormal, even good packings can lose a little bit of water.

What type of system are we talking about? baseboard? radiators?

What is the highest heating emitter piped above the boiler?

My thoughts on this is that you are forming a vacuum in the system at a high point which is allowing air into the system. As pointed out by @mattmia2 the first takeoff after the spirovent is the black circulator which is the offending circulator. Putting cold water back into the system from a leak you can't identify does not put that much air into the system if its just replacing what you are losing. There would be a constant deaerating of the system providing the spirovent works.

Now if you have the highest radiator sitting at just the fill pressure in the system then there is a chance every time it cools it will pull air back into the system. I used to see this a lot earlier in my career. Direct return radiator system would heat up and be fine but then the summer would come, the system would cool down, pressure drop, and then all the air vents or packing on the valves would allow air to slowly creep back into the radiators on the top floor. And of course all the circ's are on the return so you don't have the luxury of having the circulators help you bleed the system.

i would bleed these big brownstones all the time until i realize what was happening. Year 1, boss never goes to the job so he's no help. It's something you figure out on your own because you know somethings not right and systems constantly air bound should not be happening.

my method was to leave the fill on for a month or so when first started, return for a checkup and consider closing the valve then

Most mod cons have pressure or flow protection, typical cast, maybe not

Solar thermal systems do not have fill systems and they see wide temperature swings to boot.