Mr Wiz gets it. It is all about the inverter alarm. Some 12v inverters have an 11v alarm and 10.5v shut off. Others have no alarm until 10.5 shut off ISTR. They also specify a range above or below that where it will go off so it is luck of the draw what yours is.
It appears one 24v inverter has that 22.3 alarm, so you get a little more wiggle room than with 11 at 12 before it goes off. But you might get that wiggle room with a different 12v too.
Meanwhile the real voltage for the alarm depends on your wiring between battery and inverter because the inverter goes off depending on what voltage it "sees", not what the battery voltage actually is.
So that can skew any comparison between 12v and 24v for when the alarm goes off.
From all this, I don't see where it is "worth it" to go 24 vs 12 if you are getting it done at 12. If you can run the microwave while the batteries are at 50% that's all there is. You will be recharging those batts now anyway.
If you can't run your microwave at 50% SOC, then going 24v isn't the cure. Just add batteries or use fatter wire from inverter to battery. That has to be easier than going 24v and buying new inverters, etc.
Exception might be a small RV where you can't add space or weight. In that case, go AGM vs Wet. The 12v AGMs have much lower voltage sag so the inverter will not alarm so soon as with 6v Wets. You can carry two 12v AGMs and do as well with high voltage draws as with four Wets. Of course you only have half or less AH in the bank, so you need to do a 50-90 recharge every day instead of every second day.