I've never noticed such slime from zoas, but did have slime coming from anemones before.
I don't think zoanthids use alleolpathy like that. They do push other sessile invertebrates and take over by pressure, but if they release chemicals in mucus or similar, it is probably minor. We do know that some Palythoas and Protopalythoas have slime and that is obvious. Probably for defense and to help remove debris from their structure.
Some times I've noticed a small line around some colonies, like the extreme polyps were sweeping around for expansion. The lines are basically an area around the colony without algae, formed because of the polyps were blocking the light. The lines can be seen when the extreme polyps are partially retracted or not fully expanded. I don't think chemicals were involved though. They tend to push the algae away and clean around to expand the colony that way, slowly. But most of the time there is lot's of algae and other zoanthids touching the colonies. There are soy corals, sponges and algae that can grow together with zoanthids.
Your carpet anemones will release mucus, as allelochemicals.
Grandis.