Connecting a voltage meter to the battery positive and negative terminals will only give you a headline voltage that is currently in the battery. This figure cannot be relied upon to actually show the health of your battery.
However, should it display a voltage below 12.4v then it is highly likely that your battery is either not fully charged or defective.
What is required to fully understand the battery health is a load test.
A load test will show you the true voltage / level of your battery whilst a load is applied to it.
This can be achieved by using a battery load tester if you have one, or alternatively have one carried out for you at a battery specialist.
Another simpler way is to go to your heater controller and with the heater OFF.
Note the figure displayed on the main controller screen top right. (Refer to above chart for battery health at rest and correct if nessesary)
Now start your heater and again watch the voltage screen on the controller, this will give a live reading of how your battery is performing under the 9 amp start up load of the heater. Refer to above chart for true health of your battery during this start attemp.
If it is 11.5v or below 11.5v your heater WILL NOT START. Correct battery issue and retry.
Whilst the reading is accurate it still leaves 2 possible issues, 1 the battery itself and 2 the negative grounding to the vehicle chassis.
Further testing would be required to correctly diagnose the issue. A degraded chassis earth is a possible cause and needs to be eliminated prior to replacing battery.
Your heater takes its negative connection from the vehicle chassis, thus a degraded negative battery terminal to vehicle chassis connection or heater negative to chassis connection can cause issues on low voltage being displayed. Both need to be tested.
If your heater controller screen is blank and your battery is fully charged it is highly likely that the issue is the negative connection or the inline fuse for the heater has blown.