Search coil with ferrite not working
No it won't pick anything up as you saw. In any direction and, in any prevailing magnetic field, the lines of flux will concentrate in two halves of the ferrite in the same direction and, you will get cancelling voltages induced: -

Thus, flux entering from the left will congregate in the shorter paths and use the ferrite core to do so. This will produce equal but opposite voltages in the turns around the top compared to the turns around the bottom.
Flux will exit and start to spread out again but, there will be no net signal in your receiver coil. Ideally, you need something like this to enhance the flux and voltage sensitivity: -

The big red centre is a piece of solid ferrite but, you could use your toroid to prove this.