Can you harm battery by pressing down too much?

You should be fine, usually when you use sharp objects, it starts to get a little sketchy. But if you just pressed down with your fingers, you are fine and don’t need to worry about anything. The only factors that can harm a battery if pushed down with fingers are, pressing on the battery while having a bent housing (needs to be pretty bent to hurt the battery), pressing down on the cable that runs from the battery to the logic board or pressing really hard on corners of the battery. Overall it sounds like you are ok and don’t need to worry.