I'm not quite sure about that. The earths core should generate the same amount of heat (through gravitational friction and radioactive decay) regardless if we tap it or not. If the heat didn't escape somehow already it would slowly get hotter.

Whaste heat from nuclear or fusion does contribute to earth heating, though insignificant compared to any source pf c02.

But my intuition tells me geothermal wouldn't...

Mm. Actually, water vapor is a potent greenhouse gas; and that's how to covert heat to energy. So mabie it would indeed be significant.

TFA states the Cape Station plant (created and operated by a company called Fervo) are closed systems - they capture the emissions so no water is wasted or spewed into the environment as steam.

They deserve big props for this innovation and effort, as historically Utah has frequently been been treated as an industrial dumping grounds. The long-term ecological damage and visual eyesores due to strip mining, chemical dumping and other pollution is significant.

Well, that's just neat!

Oh, yes. Especially if you don't have a generous supply of fresh water, to use in your cooling towers. For example:

https://www.energy.gov/sites/prod/files/2014/02/f7/geotherma...

Waste heat is always "an issue", but rarely an issue worth caring much about.

Global warming isn't happening due to industrial waste heat - it's happening due to CO2 emissions being a massive leverage for messing with how the planet absorbs and emits heat.

Although, the more greenhouse gases there are, the worse waste heat is.