switches – How to switch a 12V power supply with 3.3V

High-current mechanical relays have too large a coil voltage or current draw and would probably fry my Pi

If driven directly, yes.

With a transistor driver for the relay coil, no.

If a relay is an acceptable (size, weight, cost, etc.) power switch, then

Select one with a 12 V coil.
Select a power MOSFET or bipolar transistor rated for at least twice the coil voltage and current.
Drive the gate or base with the Pi output.

There are one or two resistors involved, and possible a second transistor depending on the characteristics of the power transistor, but overall it is a pretty simple circuit.

Switching the load with a transistor directly is a valid option. IXYS is a big name in big transistors. The overall approach is very similar to the relay circuit.

https://www.ixys-electronics.com/

Schematics on request.