Where is stray current coming from in uA system. BLE Nano
Stray EMI gets rectified from parasitic diodes on DMM and stored in stray capacitance.  Common mode high Z EM fields can be in many volts range and on an unbalanced measurement ( low z ground, high Z signal ) result in the CM noise becoming a differential signal due to poor CMRR ( CM rejection ratio)

Solutions include raising CM impedance with a large Ferrite CM choke or BALUN around probe wire pair (clamshell or torroid) or grounding CM source of noise (shield)

Essentially this is measurement error but illustrates how Sensor amplifiers can also make measurement errors from loop antenna effects of long leads.