Thanks @bjorntocreate for your response and the follow up.
I don’t use the VPU to power either my load (LED) or the board. Instead, I only use the VS to power the INA3221 board by 3.3V from my controller. For the LED it is powered separately by different power supply as shown in the schematic. I tried both 3.3V and 5V to power the LED, but I am still having the same problem. Also, in both cases, I was using 3.3V to power the INA3221 via VS pin. Does this make sense to you?
For the VPU, I only used it when you and @Grumpy_Mike suggested to power the board on that way and measure the voltage on SCL and SDA. So, I did that accordingly. Other than that, I don’t use VPU at all. I use VS to power the board and VIN+ to power the LED. Again, when I tried both 3.3V and 5V to power the LED and measured the voltage on SCL and SDA, both read around 3.28V regardless the power supplied to the LED itself. So, I think that the voltage on both SCL and SDA is governed by the voltage provided to VS pin and that it has nothing to do with the voltage provided to VIN+ shown in schematic in the updated post.
Do you think it is clear enough? Or do you think I am still not explaining it correctly?