Is there a standard that transportation engineers use for the number of vehicles a road should carry daily for it to be widened to four, six, eight lanes, etc? Curious because I've noticed that some states seem to be unnecessarily widening their interstates to six lanes in rural areas, and others refusing to do so in places that need it.
"Vehicles per day" is a pretty bad metric to use. Instead you should look at rush hour and see how many vehicles are trying to get through.
Every lane can carry 1800 vehicles each hour on a freeway. In residential areas that is reduced to 1500. With traffic lights and priority based intersections it depends on how the lights are regulated and how much crossing traffic there is.
Having said that: the point where you are stuck in a jam is not the point where you should add a lane.
Instead you should try and find the actual bottleneck and improve that. This bottleneck is where you can start going the speed limit again. This may be an on-ramp where the traffic added saturates the lanes that are there, or an off-ramp where everyone wants to get off and that is saturating the interchange.
However just improving that bottleneck will add traffic downstream and probably create a new jam.