Did some more testing already and my impression of the instrument doesn't get better. The signal appears to get interrupted/distorted upon any timing-related change of the settings via the incremental encoder, regardless of the waveform. I attached three screenshots, the fist changing the frequency of a 5kHz sine by one least significant digit, the second the same thing for a 50% duty cycle square (now also a runt pulse is generated), and finally I change the duty cycle by 1% of the same square wave, causing the signal to pause for more than 2ms. If you use the generator to test a switch mode power stage, it easily goes "poof"

if this happens with the drive signal.
Edit: Just added a screenshot of what a frequency change looks like on the Rigol DG4000 (same for ramp; sqare & pulse similar or even a little worse than on the SDG6000X).
Edit 2: I figured out that if the -> Utility -> Phase Mode setting is changed from the default "Phase Locked" to "Independent", the Sine (and probably also Ramp) signal permit change of frequencies without the mentioned discontinuities. So in this configuration, the SDG6000X performs just as the Rigol DG4000. Square and pulse still broken, unfortunately.
The user interface will also easily ruin your day since it doesn't store the digit of the parameter that was adjusted, i.e. if you do fine adjustments of the frequency (say you're changing the 100Hz digit of a 100kHz output signal) via the encoder and then do an amplitude correction, to return to the frequency adjustment afterwards, you will be adjusting the 100kHz digit. This kind of behavior is very unproductive since especially in case of a signal generator, you're usually not looking at the generator's screen but at the screen of an oscilloscope or other test gear to observe the results of changes of the input parameters to your DUT. It must be possible to reliably change parameters incrementally without having to look at the generator all the time only to check that it's performing correctly.
The SDG6000X may have many bells and whistles but still it has to operate as a plain and simple "old" versatile fequency generator in my opinion. If it doesn't work okay in all these modes, I consider it not up to the task and not worth the money. Even the Rigol DG4000 performs better in many of these scenarios, and the best generator I own concerning this, is my cheapest one (though it's -- been -- plagued with other problems), the Hantek HDG2002B.
So far I think Siglent should focus on the details that make an instrument comfortable and enjoyable to use in real lab scenarios, otherwise (and here I remember one statement from some other thread about LCR meters, refering to some TFT-equipped poo ...) the instrument is not much more than some touchscreen-featured poo.
Even though all these issues can probably be adressed by firmware / FPGA code updates, I doubt that Siglent will take care of them all. I haven't got any experience with the SDG2000X generator but I assume that the SDG6000X's code bases heavily on the aforementioned one so I'm almost certain that these shortcomings can be found there as well (maybe someone who owns an SDG2000X could test it?). If this is the case and Siglent didn't adress these problems yet, I doubt they will do so on the SDG6000X either. I will test the generator probably for a week or two and then return it. It's not worth the money if you're not buying it specifically for its I/Q functionality (costs more money, I don't want to talk about the "liberation of options" here and now), the baseline model is just not adequate as an allround lab generator that's confortable to use. In it's current condition, I'ld rate it two stars out of five for its signal quality and fast slopes. It's too expensive for its usability value.