Not particularly ESF, but a typical "play visit" is basically to see where the child is "at" in development. Kids have a choice of zones to play in, and normally have a trusted adult with them. Name tags are likely to be given for accurate identification of the children (and adults!). Teachers will probably be wandering around with clipboards taking notes on such areas as verbal skills (and which language the child uses), coordination and social skills, concentration and zones chosen.
In the school I worked in, teachers did not usually speak directly to the children, as we did not necessarily expect them to have reached a stage where they could interact comfortably with strangers.
The teachers will be very aware that children's abilities, skills and interests are developing VERY rapidly at this stage of their lives, and will be taking this into account when considering the differences between children who are only 30 months old and those already 3 years or more.