Most journalists have specialties: sports, international affairs, economics, etc. Some get be quite specific. Reporters may specialize in the tech industry, or just on some narrow aspect of the tech industry (electric vehicles, social media, etc.)
Presumably a "climate misinformation reporter" is one whose assigned beat is misinformation about the climate. There are already reporters who specialize in climate change. Climate misinformation is a big subset of that -- what misinformation is spreading, how it's spreading, where it's coming from, why it's wrong.
Perhaps it's their full-time job, or perhaps it's just one of several hats they wear at the BBC. I'd be curious to know whether they associate their jobs more with the climate reporters or with social media reporters. Perhaps there's enough overlap that they needed to dedicate somebody to work with both.