This is information provided by Umesh Mandal that explains about the "Bihari group of languages" in relation to the Maithili language:
Kellogg (1876/1893) and Hoernle (1880) regarded Maithili as a dialect of Eastern Hindi; Beames (1872/reprint 1966: 84-85), regarded Maithili as a dialect of Bengali, Grierson has done a great service to Maithili language, however, he erred when he gave a false notional term of "Bihari" language, after that western linguists started categorizing Maithili as a dialect of "Bihari" language; although there is nothing known as "Bihari Language" and both Maithili and Bhojpuri are spoken in Bihar (of India) as well as in Nepal.Umesh is working on the localisation of MediaWiki for the Maithili language and as this language is currently in the Incubator, the language committee does its due diligence and tries to understand if Maithili can have a place in the Bihari Wikipedia. The information provided by Umesh makes it quite clear: "no".
This still leaves us with the misnomer that is the Bihari Wikipedia. Apparently the language used for the localisation and the articles is Bhojpuri. Bhojpuri has the ISO-639-3 code "bho".
Are you still following all this? Ok, there is one question I am not asking: How about the Kaithi script?