What is a 通信{つうしん} from a manga publisher?
According to a search on jisho.org, 通信{つうしん} by itself can mean "correspondence," "communication," "transmission," "news," "signal," or "telecommunications."

However, further down the page (the third entry), there is another word that combines 通信 with 販売{はんばい} ("sales," "selling," or "marketing") to form 通信販売{つうしんはんばい}, which refers to any kind of mail order service (including shopping online and getting a delivery by mail).

Taking my best educated guess, these booklets are likely a promotional item or extension of the magazine distributed by mail, and 通信 is used as an abbreviation for 通信販売 (as that compound seems to carry the most relevant meaning to this question).