Laser power settings of 10, 20, and 30% obviously produce different results:

However, the scope traces for PWM values under about 25% all look pretty much like this:

Rather than a simple constant current source, the power supply produces very high amplitude current pulses for low PWM inputs, with no visible differences between any of the PWM values.
The scope can compute the RMS value of (a section of) the trace, so I aimed it at traces captured from the upper left block of this test pattern:

Because the pulses have such a high amplitude, I set the Tek AM502 current amp at 100 mA/div to capture the entire pulse. Measuring a part of the trace without a signal gives the baseline noise level:

The scope display is 10 mV/div, so 1 mVRMS (close enough to the 894.4 µV reported just above the bottom label row) means 10 mARMS of noise. Given that 100% PWM corresponds to about 25 mA (DC-ish during the pulse), the RMS numbers may not have any significant figures.
A slide show of the results so you can page through them:
The RMS value comes from the trace between the A and B cursors.
Extracting the numbers:
- 0% PWM → 1 mV → 10 mARMS
- 10% → 2.3 mV → 23 mA
- 20% → 2.0 mV → 20 mA
- 30% → 3.0 mV → 30 mA
- 40% → 2.3 mV → 23 mA
Which says I’m measuring either too much of the wrong thing or not enough of the right thing: there may be no baby in this particular bathwater.
But RMS is meaningless on an aperiodic function, isn’t it? What you really want is the area under the curve so you can compute amp-seconds (and then, I guess, measure the tube voltage to convert to watt-seconds aka joules)?
The Siglent manual is downright vague, but I’m pretty sure the scope computes the RMS value inside the gate = “the period”, much like we pretend an FFT computed from a set of samples means something. Given the tube current is uniformly positive, the mean value might be equally useful.
The scope can also compute the true integral of a waveform inside (another) gate, but that’ll require some dedicated fiddling and incremental setup save / restore progress.
The error in my assumptions: the beam power definitely responds to those spikes, while the average power output starts right after the first spike and continues more-or-less evenly during the whole cut. I know nothing of gas laser physics, but the lasing action seems to depend more on getting the gas excited and less on how much oomph was applied to get there.
Seems reasonable to me. You probably can’t go far wrong treating it like an overgrown neon lamp – high voltage to strike the discharge, then go into current-limiting once the tube resistance turns negative. Hopefully the area under that initial spike is small so it doesn’t much affect the total power delivered over the entire interval. But I still think RMS is the wrong hammer — and that current waveform still looks terrible. :)