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The TL431 is a programmable shunt regulator (rather like a programmable Zener).
It starts to conduct current, cathode-to-anode, when the voltage at it REF pin (junction of R2 and R3 in your circuit) goes above 2.5V.
When it conducts, then it sinks current from R1, thus reducing to base current...
A low-cost (<U$2), rail-rail I/O general-purpose CMOS op amp with very good specs is the TLV915x, where x is 1 (single), 2(dual), or 4(quad).
It has an offset voltage of 125µV, 4.5MHz GBW, 10.5nV/√Hz noise, and 20V/µs slew-rate.
It won't be when using a resistive divider for the sensor output as you have.
If you want a linear output then the PT sensor needs a constant-current source, as the circuit in post #13 does.
Some ways of doing this are by using the sensor as the inverting op amp feedback resistor, or driving the...
You can use a resistive divider at the output of the capacitor from a V- supply to ground to set the DC average level at the value that occurs when the circuit is operating.
As noted the drop is logarithmic with current.
At 25°C the drop shown is about 0.2V for a two order of magnitude drop in current, so the drop from .01mA (10µA) to 100nA should also be about 0.2V, giving a forward voltage of about 0.2V at that current.
Below is the LTspice sim of a similar diode...
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