GA Drilling was pushing plasma drilling back in 2018.[2] They're still pushing it, but not making holes.
The University of Minnesota was pushing electro-pulse boring in 2015.[3] Again, no deep holes.
There's something called ThermoDrilling, which, despite the name, is more like a water jet cutter.[4]
Successful projects are still using mechanical drilling.[5]
So there are a lot of deep hole drilling approaches being studied. Anything that works would be used by the oil and gas industry, and if they're not trying it, one suspects it might not be working.
[1] https://www.researchgate.net/publication/270653673_Microwave...
[2] https://www.gadrilling.com/
[3] https://experts.umn.edu/en/publications/electro-pulse-boring...
[4] https://www.geodrillinginternational.com/deep-geothermal/new...