2019 Honda Insight EX
I had a feeling whatever algorithm Honda set for the Insight will always put priority on battery lifespan. Your explanation helps to explain the weird logic behind the battery sometimes not charging or being used. I'm guessing the car also has a hidden battery reserve that we don't see even when the battery indicator shows full charge/low charge similar to how the gas tank has a hidden reserve even when the display audio tablet is showing 0 miles left in the tank.I can actually answer the battery question with relative confidence.
Three very important numbers. (I don't have access to the battery pack information, so doing this as a general statement)
Soft Cell Cutoff- This is the lowest voltage that the battery can discharge rated amperage, and is considered effective at.
Nominal Voltage- The natural homeostasis of a battery.
Maximum Voltage- The highest safe charged level for a battery.
When a battery is below nominal voltage, it actually wants to charge. This is why the battery seems to charge fastest from 2-6 bars.
Once a battery hits nominal voltage, it'll still accept a charge, but is less willing to do so.
As a battery nears maximum charge, it's more resistant to charging. Also as it nears this, the rate at which it'll charge decreases. As part of the charging system, it'll essentially trickle charge at this point.
Example. Sony VTC5 18650 battery.
Hard Cell cutoff 2.7v, soft cell cut off 3.2v Nominal Voltage 3.7v. Fully Charged 4.2v
If I throw a battery on the charger at let's say 2.7v and another at 3.2v. They will both charge to 3.7v on 1 amp of current in less than 2 hours. Once at 3.7 the charger will stay at 1 amp of charge until 4.0 volts. This will take approximately 2 more hours. Above 4.0v to maximize the lifespan of the battery, the charger will start dropping charging current. It'll take approximately 2 more hours to achieve that last .2 volt charge.
You could charge the battery faster, and force more charging current, at the expense of battery lifespan. Also it'll generate a lot more heat.