A hyd line might be rated for 3500psi, but that doesnt mean it will burst at 3501 psi. A hyd pump might be rated to make 3500psi, but that doesnt mean it wont build 4000psi. There is a certain safety factor figured into the recommended rateings. Spikes in pressure can and do occur. Those spike's in pressure can and do cause hose's to burst and pump cases to crack, hyd cyl to swell and split. When looking at the CV relief in the pics, it looks to me the relief screw has been screwed all the way in. There isnt a acorn nut covering the relief screw and its probably because the relief has been screwed in so far the nut wont screw back on. The slot in the screw is even distorted suggesting the relief was probably bottomed out, and most likely wasnt letting letting oil bypass at any pressure. So If the engine had enough power to pull the pump at 4000psi, then it is very possible the 4000psi pressure reading is correct.
Air in the gauge line will compress, but it will still read how much pressure is present. A hyd system doesnt pump a steady rate of pressure. Pressure only builds as resistance is met. Because air can compress more than oil, a sudden spike in pressure might make the gauge reading off or fluctuate or bounce, but if steady pressure is applied the gauge will read correct, even with air in the lines. Even hyd oil will compress, altho not to the same degree as air. Water will compress also, even tho water and oil are considered non compressionable liquids.
Air in a brake line would act differently than air in a hyd line. This is because of the limited amount of brake fluid flow. A wood splitter pump is supplying a unlimited flow of oil as long as the pump is turning. A brake fluid flow is limited by the size of the piston in the master cyl and the lenght of the stroke of the brake pedal. Once that pedal is pushed, what oil is flowed, is all the oil there is going to be and air is taking up space in the lines, this would equal spongy pedal and no brakes. If you could supply a steady supply of brake fluid to the wheel cyl, then the brakes would work, even with air in the lines. Air cyl and motors work on the same principal, supply enough air to the cyl and it will extend and build pressure, a motor will turn and build power