What it sounds like to me, is fuel pump.
Pressure leaks down over night, then first start in the morning, it takes a few seconds of cranking to start the motor, instead of instant start.
Rest of day it holds enough pressure for instant start.
Funny you should mention about batteries. I put mine on the charger Saturday. The charger is a ctek mxs5. When l put it on, only came up 3 lights out of 8. Reading the manual on it, says you can start the car from 4 lights. 7 lights is fully charged, 8 light is checking that the battery will hold charge. Didn't get that far. I charged it to 7 lights
Mine was starting on 3 lights. If heater or aircon was on, it would take a few seconds for hvac motor to kick in. The engine would start instantly.
Yes l think its better. The engine & hvac motor starts instantly now.
I'll have to get in the habit of putting the battery on the charger every now & again.