Solar panels can sit in the sun without producing any power at all just fine. The sun will cause a voltage to develop on the solar panels output terminals, but if that voltage is not enough to cause current to flow, for example, because of battery charge controller is not drawing current, or because they’re not connected to anything, nothing bad happens.
I don't know if OP's inverter supports it (looking at the manual real quick shows that it should), but the one I have will let you set any loads to use the battery when it's fully charged. Then set a point when it'll switch off battery, say 90%, and use the excess solar (after loads) to charge the battery again. So keeping the battery between 90%-100%, while still using most of the solar.
I don't have any loads setup on mine because I don't want to run cables everywhere like that, so my battery just sits fully charged until I need it.
