Induction-Heating-Circuit not drawing any Current

I think you dont need L1 and L2...only the work coil and the resonant 
tank cap in series or parallel. You have a series oscillatinc circuit.

the gate resistors are a bit too high...acc. to the datasheet, they use 
a 10 Ohm Gate resistor for the given switching times. I also suggest to 
use a gate driver with more power, 160 mA is too less. You want to 
switch the IGBT´s fast which results in less switching losses for 
IGBT´s.

For my induction heater, i use a STM32 for controlling and a MCP14E10 
for gate driving with a GDT. The MCP14E10 can deliver up to 3 A.

The energy will wasted in the LC circuit with no load (iron, etc.) in 
the coil.

at idle (no load in the coil) and control with resonant frequency, a 
series resonant circuit pulls the most power, where a parallel resonant 
circuit will pull at least power at resonant frequency.