What could be the issue with energy monitoring IC (HLW8012) and my non-isolated power supply?
Yes you will have a ground issue with this circuit. The problem is that the GND of your circuit is a local ground. That means local to your circuit. If your circuit is powered on then the GND in your circuit will be at roughly half of the mains voltage.

That means that if you connect this circuit to a PC, it's case would become live at half mains voltage. That is extremely dangerous and that's why PC cases are (or should be) grounded via the mains earth connecttion. This means that the PC's mains earth connection will short your circuit's ground to mains earth. Your power supply circuit is not designed to handle that so it blows up.

You really need to study the subject of mains isolation, why it is needed (safety) and how it is done (transformer, opto couplers, wireless).

Then browse the internet for similar (mains power monitoring) projects to learn how it is done. You will find that monitoring mains current directly via a shunt resistor is always a challenge. It is much easier to use a current transformer or a Hall sensor based module as these already provide mains isolation so they're much easier to use.