I may be all wet here, but from the data sheet:
"Slow or inaccurate responses can also occur when the reference pin is not provided enough overdrive voltage.
This is the amount of voltage that is higher than the internal virtual reference. The internal virtual reference
voltage will be within the range of 1.24 V ±(0.5%, 1.0%, or 1.5%) depending on which version is being used.
The more overdrive voltage provided, the faster the TLV431 will respond. This can be seen in Figure 27 and
Figure 28 where it displays the output responses to various input voltages.
For applications where TLV431 is being used as a comparator, it is best to set the trip point to greater than the
positive expected error (that is, +1.0% for the A version). For fast response, setting the trip point to > 10% of the
internal Vref should suffice.
For minimal voltage drop or difference from Vin to the ref pin, TI recommends using an input resistor < 10 kΩ to
provide Iref."
If your V1 is 2.9V, then the ref input is just setting at ~ 1.234 V,which is ~ equal to the internal reference, therefore sluggish behavior.
Try changing the divider to Vref and see what happens

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