I think the beach control panel doesn't show the battery condition unfortunately, but there are cheap ways to tell.
Waeco Fridge (its more efficient than the VW one anyway) and heater we can easily go 3+ days in my beach. Never ran the heater full time so can't really comment on that however. Longest on battery was 6 days for us and it has some capacity left.
My personal opinion if you run your battery down to 10.8 it would do damage to it and may never charge as well again. You don't really want it below 11.8v to avoid damage problems is my view.
Very rough guide here:
100% 12.70 - 12.8+
75% 12.5
50% 12.35
25% 12.00
0% 11.80
There are several options:
A cheap 12v socket volt meter, will give you a rough idea of how full your battery is based upon the above chart. Batteries will display different voltage under load which is why this method isn't always as clear.
If you want to know the capacity you need something a little more expensive that can tell you amps going in and out.
You can install something like this which has no screen and you use your phone to view the battery condition. After a few holidays using it, we were quite in tune with our van and use it less.
https://vwcaliforniaclub.com/threads/nasa-bm-1-bluetooth-review.20041/
Or a victron battery monitor or equivilent. BMV 700 or similar is another favourite. They also do bluetooth versions..