Leaving a Lithium battery on the charger and constantly charged to 100% will degrade the battery over time. The warmer it is the faster it will degrade. Over what time? That is impossible to say exactly. I would expect the battery being shot for the purpose of powering the device on battery in a year or two. Some devices will not power on without at least a minimally functional battery The degraded battery may be good enough for that to run on the power supply.
Not much you can do about it except put the power supply on a timer with intermittent cycles of on and off that keeps the battery charged between about 50 and 80%.
Running the battery down to a few percent and recharging it fully degrades the battery even faster.
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