The HT7A6322 has a fixed 60KHz oscillator - it shouldn't change depending on load.
I think the problem is that your load is very light. It is drawing almost no current, causing the regulator to go into burst mode to keep the output regulated.
It runs at 60KHz for a bit, then switches off until the voltage drops, then runs at 60KHz again. Repeat constantly.
The bursts occur at a rate that depends on the load. The inductor likely vibrates in response to the bursts rather than the switching frequency.
To make it quiet, you could try a different inductor. You could also just live with the higher current consumption needed to keep the regulator out of burst mode. Your 1.2k load resistor only draws 10 mA amperes of current, wasting 0.12 watts of power.
Alternatively, find a regulator made to work with extremely low loads.
Please do remember to keep that circuit in an insulated housing with no user access to metal parts from the outside.
Your circuit is not isolated. There may be only 5V and 12V between the outputs and the circuit ground, but the output ground can be at line voltage depending on how the outlet and your power plug are wired.
That circuit can kill anyone who touches any conducting part of it.
There is a design for an isolated power supply in the datasheet. Consider using it instead of your unisolated circuit.