Between neutral & earth? That's surely going to depend on the topology of your earthing system [0] - TN-C will be so low impedance you won't get much through your deliberate load at all, more with TN-C-S, but most luck with TN-S where neutral already has a long cable run full of impedance before it joins back up with earth, and you can add a small enough load that that path gets a non-negligible share of the current.
Even device's own ground plane some times works. Though, it's near impossible to do with isolated power supplies. Modern ULP MCUs are incredibly power efficient, and can run for a day on a power of a single LED blink.
Anything wireless is still out of the question unless real ground is there though. Without ground, a dedicated power harvesting circuit would certainly provide more power.
We experimented with harvesting, with 10cm antennas, it's just enough to do a single beep once 20-30 minutes using specialised ULP UHF radios, or RX for a few seconds once a minute.