I wouldn't think the charger would be connected if the battery is in standby as usually everything is disconnected from the battery at that point.
Typically a lead acid battery is 100% charged at 12.6V, 50% charged at 12.2v and fully discharged under 12V. However, the voltage test is only accurate on a disconnected battery at rest for at least 1 hour with no load or charger connected during the rest period (24 hours rest is better, but 1 hour gives you a reasonably accurate reading).
12.3V to me indicates a somewhat discharged battery.
Battery charge voltage is typically around 13.5V or so. If your DC converter was hooked to the battery and on shorepower, you should measure 13.5V or higher (depending on the converter charge mode), which would indicate the shorepower converter is maintaining a charge on the battery.
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