I tried to replicate your findings (SDG6022X, "liberated", F/W 6.01.01.36, H/W 03-00-00-78-38) + DSA815-TG. I couldn't find any of the significant sampling frequency feedthrough superimposed to the signal (100mV standard deviation, 0V offset, 50 Ohms load impedance, no bandwidth limiting). Moreover, at Nyquist frequency (600MHz), it shows a dip and at 300MHz, when deliberately searching for a signal, there was something to be found (please be aware that the DSA815's lowest RBW is 10Hz), but considerably below the generated noise level at 100kHz RBW, that's why it wasn't observable at these settings.
It's difficult to tell exactly what may cause this discrepancy, it could be related to (a change in) Siglent's oversampling approach or possibly a modified reconstruction filter configuration. Can you check overshoot of 1ns and 2ns rise time square / impulse edges on your AWG for comparison?
Edit: I guess I've got to revise my statement from yesterday a little: I re-tested your setup again today since yesterday, my preset noise level was higher than yours. I changed the standard deviation to 48.4mV which should approximately match your settings and -- indeed -- I found some of the feed-through at 300MHz, though considerably less than what seems to be present on your AWG. Moreover, the noise "passband" spectrum on my AWG seems to be slightly flatter and the drop-off shoulder seems considerably steeper which really makes me believe that Siglent may have modified the reconstruction filter. I didn't find any noticeable difference between the two channels, moreover, enabling the "idle" channel with maximum output level of 300MHz sine doesn't change the figures of the noise channel being tested. See the third screenshot for details.
Edit: Typo, Clarification, Add-on