My church? We run right around 5000.
The duties of our security team are pretty much as you say we direct traffic in the parking lot, watch the children's church area and watch over the playground if the kids go out.
We also have someone drive around the lot and deter vehicle break ins (Pastor's car got stolen right out of the parking lot last year). Make sure doors are locked and follow the ushers when they empty the collection boxes at the end of service. (Our church doesn't take a public offering we believe your giving is between you and God and we have collection boxes at various places throughout the lobby to facilitate that).
We also act as bouncers if someone disrupts the service.
New Life Church (not my church) has a ministry devoted solely to helping other churches set up their security teams and helping pass on lessons they learned when they had their active shooter incident. The head of security at my church worked very closely with them when setting up our security ministry and we were very careful to stay within the bounds of Colorado law.
Pretty much what I thought. Others are overthinking this . . .