The burner looks like it has two issue. The rattling sound is an oscillation, the pulsing is from too high a velocity of the gas. The burner should have laminar gas flow, yours is turbulent.
The first thing to check is to make sure there is nothing blocking the jet/orifice. I had a spider web inside that tube once and it ran crappy.
The jet should have a round hole, no blockage or corrosion.
If the gas stove burners look good then I would think the pressure is OK.
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