Ideally get yourself something like a BM2 battery monitor. Failing that get yourself a plug in monitor that will give a voltage reading from the 12v socket.
If you are on the original AGM battery I would not be surprised if it's near the end of it's working life if previous owners haven't looked after it.
Basic rules with AGM is aim to recharge as it drops below 50% charge, that's around 12.0v for traditional lead acid or AGM - the built in meters can be famously inaccurate as to what the colours actually mean so try and check it against something that shows actual voltage - and measure that voltage at rest as it will drop slightly under load.
I put a lot of battery background over on this thread that might be a good place to start if you want to delve in a bit:
Hi all, I'm new to forum and to campervan ownership. We have bought a new T28 conversion and would like to understand the battery and charging setup. The items which depend on the battery in our van from the top of my head are: Fridge; Heater (its run off diesel but has a fan); Lights; Water...
www.t6forum.com
And as to mains charges while I think many campsites are still traditional fixed fee as they don't have metering equipment in my other life coastal and inland marinas have generally been on metered EHU for a very long time. I'd fully expect as equipment is replaced it will be replaced with metered equipment and it will become more common.