I removed C21 27nF , the input LPF capacitor , and for measuring resistance seems to be no change , exactly the same instability ... so it is not used by firmware in my opinion . Or if it is used the effect is very weak .
In this case DC ranges become unstable , picking up the noise , as should be expected without it . For measuring DC that filter is useful , no doubt .
I added a 47nF capacitor ( first value I found ) from PB0 to AGND ( ADC input is PB0 - PB3 connected to AGND with 10Kohm ) and now there is first some charging effect ( big capacitor and low measurement current) but then the resistance value is pretty stable and you can move the probes around , touch them and the tips . No worries
. More or less like other multimeters .
In the HY3131 configuration document for measuring resistance it is clearly shown that this capacitor must be used , the red one between FTP and FTN pins . I'm not sure what that selectable resistors 100K , 10K and 0 (short) do , are in series with this capacitor or not ... if they are in series than 100K + 27nF may not be such a good filter for cutting down strong AC 50Hz induced noise ... than 10K or the capacitor directly connected at input could be selected.