Auxilary battery voltage? Does the Prius do 2 stage charging?

This is a long story but I'll try to shorten it. My 100 % recycled 2012 PIP was totaled by being "T Boned" by an inattentive driver. The other driver's insurance paid for my replacement, a 2013 PIP with a few less miles and no damage history. On the drive home in the replacement I used way more gas than I was used to, about 100 less miles per tank. I started searching for the cause. First I Installed the lower grill block next I changed the oil and air filter then I replaced the snow tires with Bridgestone EP422+ inflated to sidewall limit of 51PSI, then I found dragging, badly worn brakes and replaced them these changes helped a little but something was still very wrong. I replaced the dying but not dead 12 volt battery with 40 AH of LIFEPO4 and continued my search for a possible cause. I'm very sure that I finally found the culprit based on trip odometer data over several short trips after I cleaned the mass air flow sensor. I run the Android application "TORQUE" through an OBD -Bluetooth adapter and look at several interesting things, among them the 12 volt system voltage which I kind of assumed was always 14.4 volts whenever the car is "running". But with the new 12 volt battery I'm seeing something I've never seen before, When I first turn on the car the voltage will be 14.4 but after some running, in the daytime, it will drop to 13.3 but turning on the headlights will move it back to 14.4. My interpretation of this observation is, Toyota has implemented a form of 2 stage charging for the auxiliary battery. The 2 stage charging algorithm is something like, hold 14.4 volts until the charging current falls below set-point 1, then drop the voltage to 13.3 (float) until the charging current exceeds set-point 2 which resets the 14.4 volt system voltage. Has anyone else observed this? Can anyone verify the 2 stage charging?