Is it safe to charge and use the battery constantly? Is it a standard
use case, can't it reduce its lifetime?
Depends on the charger. A good charger will will have a setting for type of battery, battery cell voltage, and have three charging stages.
- Constant current
- Floating or hysteresis
Chargers charge beyond the nominal battery voltage then float down to the nominal voltage. Keeping the battery at the topping charge for more than 48 hours will harm the battery.
Many cheap chargers deliver only a topping charge. This would not be good for your application. A topping charger should be disconnected after 60 hours to prevent over charging. If your charger has a floating or hysteresis stage you should be okay.
Once fully charged, the battery should not stay at the topping voltage for more than 48 hours and must be reduced to the float voltage level.
This is especially critical for SLA
because they are less tolerant to overcharge than the flooded type. Charging beyond the specified limits turns redundant energy into heat and the battery begins to gas.
Source: Battery University