Depends on which size Provari you get. The Mini uses an 18350 standard, or an 18490/18500 with the extender. The regular Provari uses the 18490/18500 standard or the 18650 with the extender.
I don't have either, but I have a VTube that uses the 18650 and I can vape all day long and still have the battery at 3.8 volts at bedtime, which means I could get another 1/2 day out of it without charging it (or more if I wanted to run the battery down even lower).
The 18490 is an 1100mah battery, so it should last 10 - 11 hours of normal
vaping. The 18350 is 700 or 800mah I think, so that should translate to 7 or 8 hours. But that's just a rule of thumb and will vary depending on your
vaping style - frequency and voltage.
Also, cheap knockoff
batteries will generally not last as long between charges as good quality batteries like AW or Panasonic.
I don't think the LED screen uses much power. I think the power consumption comes from cranking up the voltage.