its like a butterfly valve.
Those rods are just for tuning. Cheap designs use bolts, this one did it a nicer way.
This circuit really makes you wonder, the wavelength is 1/2 meter long.
It looks like when you turn the apatures, there is more or less of the waveguide 'visible' to the antenna stub (waveguide to coaxial transmission)
Is there a electrical contact between the apature and the stub, or is it a big wide hole without contact? Post a picture at an angle
I tried to think about it in terms of waveguide E and H fields. The rectangle apature looks like how you would draw the H field of a wave guide. Does it agree with the polarization?

Those rod are helping impedance match the irregular shaped cavities?
Because most waveguide launcher, the wave is inserted in the wide side, or the end, this one is narrow side

is that a h-plane translation?
and what do you call those shorting screws? Does the adjustment of that work like a collar that is pulled up on a screw?
or is it this? capacitors

water pipe type coaxial resonance capacitor?