Old phones with that streaming software run hot, in my experience, so this is certainly very sub-optimal for the battery and safety compared to just normal use.

Old phones with that streaming software run hot, in my experience, so this is certainly very sub-optimal for the battery and safety compared to just normal use. Having it plugged in, OTOH, probably doesn’t matter. There’s safety IC to prevent overcharging. Actually fully draining, mechanical damage, water damage etc. are more dangerous, which can happen during normal use anyway.