I had noticed the same issue a few weeks ago when mapping the town border.
According to 马祖资讯网 (https://www.matsu.idv.tw/topicdetail.php?f=4&t=126949), it is not a part of Matsu Islands; according to 连江县志 by 连江县地方⽅志编纂委员会 (mainland) page 152, it belongs to 苔菉. Very few information related to this island were recorded by Taiwan. This island is not inside 限制/禁止水域 of the Taiwan region (海洋法令汇编 page 叁-一〇、 叁-一四、叁-一五) as 刘泉礁 and 东沙岛/南引岛.
The island was labeled within the maps from https://spatialplanning.matsu.gov.tw/ . For the special region maps by the mainland government, it is a part of the special region as the you can tell from the name "连江县东引岛、西引岛、黑岩岛、东沙岛、马祖列岛区域地图".
However, this island does not exist in the 公告土地现值及公告地价 by 连江县地政局 (https://www.matsu-land.gov.tw/chaspx/Search12.aspx?web=34), but 刘泉礁 and 东沙岛/南引岛 were included. Also, the dispute discussions of this island does not exist, unlike 刘泉礁 (https://www.matsu.idv.tw/topicdetail.php?f=2&t=249169) and 东沙岛/南引岛 (https://www.chinatimes.com/realtimenews/20240318003616-260407).
This is an uninhabited island, which means it is not under administrations. Therefore it is hard for you to tell which side should this island belongs to in the OpenStreetMap.