ADC variable reference voltage

Use the chip MAX31865 instead.

I've been using with great success to measure PT100, the chip takes care of everything and is very easy to implement.

You only need to power the chip and provide a reference resistor, you don't need to care about anything how to drive the RTD.

It also does wire compensation (3 or 4 wire RTD) and some other internal compensation.

Total BOM cost is about 5$ all included.

Your design requires surge currents, as the ADC grabs charge for the conversion behavior. Thus the resistors, along with parasitic capacitance, need to implement a fast timeconstant, fast enough to settle to at least 0.5 degree C during the sampling interval and also during the grab-some-reference-charge as each bit of the successive-approximation-conversion occurs.

One Tau of settling provides 8.6dB improvement in measurement. Thus 10 tau, provides 86dB accuracy (other errors also exist; you must identify and manage those other errors), or nearly 13 bits.

By the way one Tau settling is NEPER.