However, there are some side effects. Iceland heavily invested in geothermal power plants and as a result their natural geysers are dying out. This is also why the US doesn't run geothermal power plants in the Yellowstone caldera, because the danger to the tourism industry outweighs the potential gains, at least for now.
We drill a few thousand meters into the crust. There's several thousand kilometers of earth below that.
What happens in practice is that such sites end up being rate-limited by either the thermal flux of the surrounding rock, in the case of dry holes which are bored and take out heat directly, or by depleting the groundwater and/or hydrothermal reservoir which feeds a "wet" geothermal project (as with California's Geysers).
Dry holes end up having a limited effective life of a few decades, based on what I've seen, after which there's insufficient thermal energy to drive electrical generation (though it may be suitable for other lower-grade heating applications). Wet holes vary in response depending on how rapidly groundwater is replenished. I believe that the Geyers has dried up numerous wells. In places with ample water infiltration (e.g., near coastlines or in wet climates), I speculate that intrusion of fresh cold water might cool the geothermal reservoir somewhat.
But the source heat, which is radiating from the Earth's core though the mantle and crust, has an effectively fixed flux. There's only so much heat radiating outwards, and a few localised pinpricks and steam generators won't effect that measurably. Volcanoes are far larger and similarly have little overall effect.
The heat is coming out one way or another. It already traveled 6500 km to the surface unaided, we're just helping it up the last 1 km or so. Frankly, I'd be interested if the core would notice an effect from the removal of the Earth's crust in it's entirety. My money is on "no for any human-relavant-timescale."
For reference, the interior of the Earth works out to about 50 TW of heat. Today, humans consume about 20 TW. The Sun delivers 173000 TW.
https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget
Which is just nuts to think about. The core is that hot and it has been for billions of years. Incredible.
So no, not 'minimal'.
My "minimal" remark was intended as a response to the question of our effect on the Earth's core; I should have made that more clear. I'm sure we'll uncover all manner of consequences to the upper crust.
Having read into your comment a bit, the USGS doesn't agree with you. :(
https://pubs.usgs.gov/of/2020/1017/ofr20201017.pdf
https://earthscience.stackexchange.com/questions/14259/did-t...
But there is an awful lot of energy there so I don't think we need worry for a few million years.