All Energy on Earth can be traced back to the Sun

Yes.

Factor in photosynthesis, without which there'd be no plants, without which there'd be no fossil fuels.

 

I would say this is mostly true. One exception is nuclear energy which traces its roots back to a star but not our sun....

 

You are right. Most of the energy used on earth can be traced to the sun. Geothermal energy cannot. Geothermal electrical plants extract heat from the molten interior of the earth and converts it to steam and to electricity. Nuclear energy is produced when fissile material generates heat during nuclear fission. That thermal energy is used to produce steam and electricity.

Electricity from a variety of sources are connected to the electrical grid and can power your toaster. Where you are determines the source of that electricity. People in Iceland use electricity generated largely from geothermal sources. People in San Antonio Texas use electricity produced from gas, coal, nuclear and wind sources.

Now about the star....

Nuclear power requires the use of very heavy fissionable elements like uranium. Uranium is only produced during a supernova event. All the uranium present on earth was once produced during a supernova event. All these heavy fissionable materials are present in the molten core of our planet and are believed to be a significant source of the heat present there now. So even geothermal energy might trace back its source to some star that went supernova in the very distant past.