You're right, there isn't much recent study of Trebizond in English...the best place to look would be Antony Eastmond, Art and Identity in Thirteenth-century Byzantium: Hagia Sophia and the Empire of Trebizond (2004), and Byzantium's Other Empire: Trebizond (2016).

Going back a little further, there is Anthony Bryer, The Empire of Trebizond and the Pontos (1980) and The Byzantine Monuments and Topography of the Pontos (1985).

Émile Janssens' Trébizonde en Colchide (1969) is also good, but it's in French.