As explained by Rohat Kılıç you need to use the proper measurement technique with the tiny ground clip, otherwise there is no way to know if the scope displays what you think you're measuring, or induction from nearby magnetic fields from your MCU into the large loop formed by the ground alligator wire.
When in doubt, always probe ground. I mean the only thing you change in your setup is to move the tip of the probe to the exact point on the PCB where the probe's ground clip or spring makes contact. Then you should see a flat line on the scope. If you do not see a flat line, or even worse if you see exactly the same trace on screen as before, then what the scope is displaying is definitely not noise on your power supply voltage.
The frequency of the noise spikes, about 40kHz, also feels like they come from a noisy USB wall wart/power supply. So if you do the above test and still see these spikes, then you can loop the probe's alligator ground clip to the probe tip, and now you have a loop antenna. Well, you already had a loop antenna, it comes for free with the ground wire, but at least now it's a useful tool instead of just being an annoying source of noise! You can move it around, and maybe you will get the same spikes when simply holding it near the 5V switching power supply or USB cables. If this is the issue, and your switching supply simply sprays its switching frequency everywhere, then it will be difficult to measure anything in the vicinity.
If you probe ground as explained above with the tiny ground spring on the probe, and you still get noise, then suspect a common mode noise issue, again probably the supply.
Regarding the importance of noise on your ADC measurements, let's check HX711 datasheet:
First things first: noise can only influence the ADC when it is doing a conversion. When the ADC isn't doing anything, then it won't care about noise. There is no way to know from the scope shot whether the noise spikes occur when the ADC is working, or when it is not working.
The ADC has several analog inputs: the signal inputs (labeled INA+/- etc) and the reference input. What an ADC actually does is compute the ratio between input voltage and reference voltage. Noise on both of these matters for the final result. So if you're interested in the ADC's supply voltage noise, you should be measuring AVDD which is your ADC reference, not DVDD which is only used for digital IO and the input of the chip's AVDD regulator.
That is of course assuming the module manufacturer didn't "cost-optimize" the AVDD regulator, but I see a SOT23 transistor and a bunch of ceramic caps on your photo, so it should be there.
Another way to get noisy measurements is a noisy signal. This can occur if wires are long, and they pick up noise from the MCU. If this is the case you can add filtering on the input, for example common mode and differential filtering caps.