If I'm just with the kids, I stand close enough to see but not right next to them. To an observer they probably don't look like there's a parent nearby, but I'm there. Often on my phone, but I know where they are. If they're on a particularly high piece of equipment (ie. above my head) I get closer but otherwise I'm pretty relaxed.
If I'm there with other adults, I talk and keep an eye on them from a distance. I haven't really paid that much attention to what other parents are doing. And if anyone is judging me then meh, I don't care.
In a full time SAHM so the park usually bores me to tears because we go so often. Give me a play centre any day where I can sit with a coffee, not watch my kids at all and read a book instead ;-)