Electronic – the difference between an injected and regular STM32 ADC channel

You must not connect a negative voltage to VREF-. The "-" only denotes that it's the lower voltage. If you check the manual, p. 209 it will state:

VREF-: The lower/negative reference voltage for the ADC,VREF- = VSSA

and for VSSA:

VSSA: Ground for analog power supply equal to VSS

Both the MCP3901 and the AD7796 are sophisticated ADCs but the first thing that marks the difference to me is that the microchip device performs synchronous sampling to ensure that when the two channels are digitized, they are "captured" at the same point in time. This is important for when used in energy management because voltage and current waveforms need to be multiplied together to calculate power and if there is a timing difference there will be a power error.

The AD7796 is just a single channel device with on-board temperature digitization and fixed analog gain of 128 making it suitable for bridge sensing. The MCP3901 has a much faster sampling speed capability making it suitable for a wider range of input signals and in particular for sampling "current" waveforms that may have many high order harmonics that must not be aliased because this can cause other "power calc" problems.

The MCP3901 also has a programmable gain amplifier whereas the AD part is fixed.

The two devices have different target applications and the microchip part potentially has the capability of performing bridge sensor digitization except it won't have the dc accuracy needed on sensitive applications.

The AD part also requires an external reference voltage and this can be chosen to be very accurate (at some cost obviously) whereas the Microchip part has a rather inaccurate internal reference but it can be overridden with an external reference.

The two devices are similar on the face of it but the devil is in the detail.