I have never been using Zeners as noise source but I think, I understand this circuit.
Does anyone have an idea why the author of the circuit boosts 12V to 34V and then drops it to 5V?
He doesn't.
I cannot see a benefit when the 7805 is a current regulator…
Current source (ideal) has infinite internal resistance so no loads the noise sorce. If you use resistor to limit current in Zener diode than in small signal circuit model you get that resistor being in parallel to Zener diode so the (probably high impedance) noise sorce model is loaded with this resistor what circuit author wanted to avoid.
The current limiter is a bit uncommon (and power-wasting) with the 7805, but not a problem in itself.
I suppose that the main circuit author goal was to get as high internal impedance current source as possible. I suppose he have tested more common solutions like transistor current source or LM317 current source and may be found that 7805 current sorce have better characteristic. Fo single transistor current source the problem is Miller effect making Ccb being multiplied by something close to beta and such 'huge' capacitance is seen as parallel to current source making this source being current at DC and relatively small frequencies but not at higher frequencies. Probably 7805 in current source configuration has smaller capacitance parallel to it. Even so at some high frequency this capacitance becomes being 'visible' so to increase the current source impedance at high frequency the ferrite beads were used.
I don't know (and don't want to search it) what MAR6, MAR3 and ERA5 are but look at their loads. In each the ferrite beads were used to increase the load impedance at high frequency. Unfortunately it is not more specified at schematic. As it is old schematic and I remember at the beginning of 2000 years SMD ferrite beads were rather expensive so may be all these are simply small ferrite beads put on wire so having about 50 ohm at 100MHz. In my circuits I am typically using 1k ferrite beads so one far away from the other. May be it is clear from the reast of publication what are these ferrite beads parameters.
Iq varies with temperature and voltage drop, so 7805 is not a great current source.
I think this is the last important parameter here.