Confirmed. Measurement is affected when battery is charging.
When charge LED stops flashing, measurement error disappears.
I tried to measure voltage between GND and VDD on ST-LINK connector.
When powered from the battery: 3.3350 V
When external power connected: 3.3306 V
After some time with ext. power: 3.3325 V (measurement error is still present)
When charge LED stops flashing: 3.3339 V (measurement error disappears)
My NanoVNA creates zig-zags on the display between 295 and 300 MHz when the battery is low or charging. Not a surprise that it's sensitive to supply voltage in that frequency range, as per datasheet the clock chip supposed to operate till 200 MHz...
I heavily suspect that the random lines occasionally appearing is also not just a drawing error but a consequence of this.
As for the torque wrench I don't think that the low frequency range and precision of NanoVNA justifies it (it's more like a waste of money and time for this level), the SMA connector can be tightened without it quite well but NanoVNA is just the perfect tool to check this.
Replacing the MCU is an interesting idea. What would be even more interesting if clock chip could be replaced with something that allows operation up till 2-3 GHz range (means mixer replacement as well...). Probably the resistor bridge would not cut it till 6 GHz but still if clocking (test signal generation) could be improved it would be a significant improvement (sure, not in this price range as significantly more expensive chips would need to be used...).
Note: When there is integer relationship between the clock source of the clock chip and its output signal is quite OK, but when I set 800MHz it's not so clean anymore (it uses 3rd harmonic, so in reality chip is set to 266.6...MHz or so)..