Get the backs of your envelopes ready, this sounds like a Fermi problem. From a quick reading of geomagnetic k-index data let's estimate the short time average flux change at 1 millitesla per three hours. That would give a maximum energy budget of 7e-5 watts per cubic metre (from dB²/2mu_0), so you're looking at picowatts of power for anything handheld.
(If anyone wants to refine this upper bound I'd be pleased.)
Of course smarter people than me have spent more than 30 seconds thinking about this and may have better answers, see e.g. https://physics.aps.org/articles/v9/91 and https://physics.stackexchange.com/questions/65082/can-the-ea...
Ballpark you're pretty much on the money .. although the standard geophysical unit for measure surface magnetic flux in surveying is the nanotesla .. with 3 axis measurements taken ten times a second at each wingtip and tail of an aircraft travelling 70m/s some 80m above the ground.
Similar but different for "long soak" fixed position magnetotelluric mapping where the field moves about the instrument rather than grid survey where the aircraft moves through the field.
https://www.ga.gov.au/scientific-topics/disciplines/geophysi...
This is related to the power question - it's all sensors moving through fields. Creating images from all that raw data is another ball of (fun) wax.
https://news.ycombinator.com/item?id=39084732
The magnetic flux near powered equipment is relatively high - one wonders if this can be pushed to power a sensor from diurnal flux - the daily pulse of a earths magnetic field at any fixed location, the measurement of which can be used for resource mapping:
https://www.ga.gov.au/scientific-topics/disciplines/geophysi...