Power measurement on multiple loads
If you do use this type of schematic from TI it should work (on a more limited power supply): -

In the comments below the question I explained why the proposed circuit won't work (take note of op-amp type and the components in the orange boxes in my schematic). Those boxed components will certainly be needed if R3 is going to be as low as 10 Ω.
Also take note that the TI design uses an OPA2376 op-amp and this limits the power supply to no-more than 5.5 volts. You need to find a rail-to-rail op-amp that has decent spec and can operate from a 20 volt supply (as per the faulty diagram in the question).
I added a few notes and basically, if you monitor V(R1) and you have accurate resistors you can reliably predict load current: -
$$I_{OUT} = \dfrac{V(R_1)}{R_1}\times\dfrac{R_2}{R_3}$$
Use a high impedance voltage monitor circuit to measure this voltage. A 1 MΩ input impedance will degrade R1 to a 0.5% lower value for instance. I'd go for at least 10 MΩ input impedance for the monitor on R1 in my schematic.
For the output voltage monitor, keep with an input impedance of 10 MΩ or greater.

Need to share the SPI bus between the DAC and the ADC, lowering the
maximum frequency I can obtain.

That's something that cannot be answered here.

Would you also consider the possibility to disable the monitoring for
open-loop control?

That's up to you. Adding a few bells and whistles is always a good thing to do at an early stage rather than try and bodge in something later on.
It's almost imperative that you use a simulator to test this before committing to a PCB layout.