You aren’t overreacting. You are being a good mom who wants to protect her baby. I agree with @Leah that you should speak to your daycare. There might be other parents who don’t like the screen time either. Maybe you can find allies to support your case if the daycare doesn’t take your concern seriously. Most of the parents I know do not support screen time for their little kids.
Oh definitely not they should not be doing this, i worked at a daycare that did this and they told us to hide it from the parents its a red flag for me
Personally I would look into other daycare options..
I would be unhappy if my paid childcare provider was doing any screen time tbh. I would have a discussion with them and share your expectations. I know easier said than done but I would also look into other childcare options if they aren't responsive to your concerns