Lets get the very basics out of the way.
According to MSI Support for the Motherboard to recognize both processors you will need to have that BIOS version or newer installed.
For the R5 5600G you will need BIOS Version 7B89v2C.ZIP or newer installed on your Motherboard. If you have an older BIOS Version installed your CPU won't be recognized by your Motherboard.
For the R5 3500X you need BIOS Version 7B89v22.Zip or newer installed. Obviously you have this BIOS version or newer installed since your PC boots up normally with this processor installed.
If you disconnected all the hardware from your motherboard except your PSU, CPU and all Motherboard cables connected and the Motherboard DIgital Code is indicating CPU Issue with just the CPU then it can be the following reason, in my opinion:
1- Defective CPU
2- Wrong BIOS Version installed to recognize the CPU
3-Defective Motherboard. This one can be ruled out since your PC boots up normally with the R5 3500X.
With your AIO Liquid CPU Cooler installed correctly your 5600G shouldn't get hot at all when booting up.
You did have the AIO connected correct? If you did and the processor still gets so hot that it burn you finger might indicate a Shorted CPU processor.
NOTE: AMD 3 Year Warranty is voided if there are any Bent or Broken pins on your CPU.
EDIT: Reading the headline for your OP, It says the processor was abruptly removed from the Motherboard.
If the processor was yanked out of the Motherboard socket it could have been damaged since now it won't boot up afterwards and the older CPU works fine.
If your PC booted up when you first installed the 5600G then you have the correct BIOS Version installed and I suggest your open a AMD WARRANTY TICKET (https://www.amd.com/en/registration/warranty-services-portal.html) unless it is still under Warranty by the Retailer.
