Engine? Battery? Something Else?

Hello. I have a 2013 Toyota Prius C One. It has 220,000 miles and was told that it's had it's hybrid battery replaced once but am unable to confirm (don't know how) but I ran checks on it with codes readers and it said battery and all cells in it are fine. It's in amazing shape with every gizmo and gadget working properly. It's stored in a heated garage at 50 degrees F (winter temps). The car has been starting to "sometimes" have worse gas mileage. It seems that it starts rougher at some starts than other times and a rough start and higher than normal throttle feeling accompanies the bad gas consumption. Good start can get anywhere from 45-60mpg and bad ones 25-35mpg. Stopping and re-starting car sometimes works. This has been happening for past few months mostly but showed some early signs of it since March. Now it's winter and the car is displaying check hybrid system after about an hour of driving in cold weather 10 degrees F. After getting it home and running some checks on it while idle it still says check hybrid system and will shut down after a bit. The 12V battery is new, and systems check says it's good. No codes of any kind or issues or bad lights. Code reader seems to think nothing is wrong all the way up til shutdown despite the hybrid warning. ALL recommended maintenance and care have been performed on this vehicle up to date with no known issues other than whats mentioned here. Although I suspect it was previously used as a Uber, I only use it for short trips once every few days.

 

This morning I had to drive my dog to surgery (about a 2 minute drive from my home). On the way there car was great but still had the warning. On the way back, the warning went away and now only says maintenance required. It seems it only shuts down when running diagnostics with code reader in it while running it idle. Otherwise it just says maintenance required.