Minimum power rail voltages for given input voltage range (inverting op-amp)
So this, I believe, gives you the minimum power rails required so that
the output doesn't saturate

Those formulas are correct under the assumption that the op-amp can output all the way to the power rails.
Typically you want to give yourself some margin though.  How much depends on exactly which part number you are using, but 0.25V to 0.5V would be a good starting point for may rail to rail output type op-amps.

Many op-amps can't output all the way to the rail.
For those op-amps that have rail to rail output the drive strength usually becomes very weak as you come close to the rails.  For example an op-amp datasheet might say something like 1mA output at 100mV from the rail.  This means that if your output goes close to the rails you won't be able to drive much load and you may not be able to operate at high frequencies.


Does it also tell me the minimum power rails needed, to ensure the
inputs don't go above/below the power rails?

In this configuration both the + and - inputs of the op-amp are held at Vref (1.67V) regardless of the input.  Note that this only remains true if the output doesn't get too close to the power rails.