Inrush is exactly what it says it is, it's inrush current. When you have a sudden surge on something, that's inrush. Lots of appliances in your home have a large inrush, much larger than the breaker they're on. Inrush happens faster than a breaker trips, which doesn't matter when you're on the grid and the inrush is lower than your mainbreaker, it matters when you have an inverter in the way with a passthrough limit and an inrush limit. Typical central HVAC units have LRA over 100 amps.

If we're talking about 'doesn't even matter with a 4kw array' well, hell, how the hell you gonna charge ~40kwh of battery with solar array that nominally produces 20kwh a day on its best day, assuming all conditions are perfect?

Backfeed is what the inverter can push out from the battery to the home. It's the size of the tube coming from the gallons of water reservoir. EG4 18k has a tiny tube, no matter how much battery you put on it. Like emptying a 50 gallon drum with a drinking straw(and with the 4kw array, filling it with a 12 oz cup).

Inrush is surge capacity. Starting a big motor like an air conditioner can require 2x or 3x the continuous running amps, but only for a few seconds.