Hi Kozmyk,
This phenomenon is totally normal. You are looking at the difference between a DSO and an analog scope. When you acquire any piece of test equipment, including a DSO or analog scope, you do have to learn it's limitations. That's why HP and Tek used to publish detailed theory of operation and schematics for all their equipment. Looking at your videos, the "unstable" DSO waveforms exactly match up with entirely comparable artifacts on the analog scope. Depending on which scope you are used to, your brain will tend to integrate out the artifacts in one, and fixate on the artifacts in the other. Also, it's why it's sometimes nice to have both scopes in the lab. But if I had to choose, I'd pick the DSO.
You are looking at a combination of several factors:
1) System noise, including at the generator output, cabling, input stage, and ADC noise sources
2) Noise from random sample jitter.
3) Signal distortion from asymmetric sample interleaving.
You can see and measure the effects of all these sources in all DSO's. High-end scopes (meaning $$$$+) use all sorts of black magic to minimize these various sources. Careful attention to input stage design, low-noise circuits, careful shielding, etc. help minimize noise. Careful clock management, high-speed ADC's, careful timing, routing, and high-speed design help with the second two factors in high-end scopes.
I've attached some images of a 16 MHz sine wave (to match your example), taken with a LeCroy Wavepro scope. The first shows sampling at 500 Ms/s, probably what the siglent is using. Here, because there are fewer samples per cycle, noise on the waveform causes more gross distortions in the perceived sinusoidal shape.
The second is sampled at 1 Ms/s. You can see distortions of similar magnitude, but half the width. The energy of each deviation is smaller. The eye perceives the underlying waveforms better.
The third is sampled at 20 Gs/s. The noise is the same amplitude, but the underlying waveform is even more apparent, partly due to the display routine, and partly due to the integrative abilities of our retinas and optic cortex.
The fourth and fifth pictures show the result of turning on persistence for the 20Gs/s waveform, and (last) the 500 Ms/s waveform.
You can see that the appearance of the high end lab-grade scope is similar to your siglent when using similar sample rates. I have tried another similar rebadged Atten scope (the 150 MHz version), and a Hantek 200 MHz scope. I found the atten/siglent to have overall much less distortion due to jitter and sample-interleave asymmetry than the Hantek. This has been discussed in several other forum threads, including the long Hantek thread, and a rigol sinc(x) thread.
So take heart. You have a great deal on an inexpensive decent quality scope, about equivalent to the low-end Tek, LeCroy, and HP scopes. Actually, identical to the LeCroy WaveAce scopes, since these are simply rebranded Atten scopes based on the same design.
Best regards,
Dave
(EDIT:) BTW, the measurements at the bottom of the screen are not meaningful, because I had them set to channel 1, and the input for this experiment was channel 2. I didn't think to switch over the measurements, and just noticed it now. Measurements would be irrelevant to the point of this exercise, however.