What takes it beyond ordinary politeness is the “take them”.
Putting it into physical space, if someone walked into the wrong office and you told them what the right office was and how to get there that would generally be considered polite. Just telling them they’re in the wrong office is probably impolite. The warm handoff is the equivalent of walking them down the hall and telling the people in the other office why you brought them there.
Having worked at a high-end hotel and on software teams with high support standards, this is very natural to me. It isn’t for others.