If I have water containing a certain concentration of salt and I boil the water to the point that I have, say, half of the initial water left, will the leftover half have a higher, lower, or equal salt concentration than the initial whole?
It will be higher. If (for example) there was 1% salt in a volume of water, then that water halved, you will be left with 2% salt content as only the water has evaporated.
This is actually how salt is made commercially. Salt water from the sea or lakes is evaporated until no water is left, leaving just the salt residue afterwards.
You will have a saltier liquid after you evaporated half of the liquid. Salt (NaCl) doesn’t evaporate at water‘s boiling point.
Just consider how sea salt is traditionally produced: Sea water is pumped into large basins and the water evaporates, up to the point where the salt concentration is so high that salt crystals can be harvested.
The same happens in your pot. If you left it for so long that all water evaporated, you‘ll see a thin layer of salt on the bottom of your pot.
Depending on how vigorous you boil your salty water, you may lose some if the salt as it gets carried away by bursting bubbles in the water and splashed around (again: white residue), but at a gentle simmer, the effect is negligible and you can easily calculate the salinity.