Your "core" is the pan and your secondary is the pan
and the secondary "burden resistor" is the pan as
well. As this is highly end-user-variable I'd think that
attention should be paid to resonance tuning for
some coupling behavior (as bounded by wallplug,
performance and regulatory realities).
You might look at industrial / metalworking
induction heaters for inverter designs, there are
many, RF LDMOS or GaN FETs are likely for the
power devices, I don't recall much thought given
to real time tuning in these applications but you
are looking also for fine heat control where dudes
melting beer cans for fun, just go full out.
You could always look for service schematics
for high end appliances. Although these days it's
probably "module level replacement by qualified
personnel".