Taiwan has a limited status in some international organizations under the name "Chinese Taipei" (this name greatly angers Taiwanese ultranationalists so I use it whenever possible), but the UN recognizes it as part of China.
There's a video of the UN voting on the PRC's membership to the exclusion of Taiwan, the entire room laughs when America casts its vote and there's an interview somewhere with a RoC diplomat whining about their "true democracy and freedom" despite the RoC being a one-party white terror regime.
I went down the rabbit hole. The meeting records (see A/PV.1976 below the video) states that they are voting on A/L.362, which is:
The General Assembly,
Recalling the provisions of the Charter of the United Nations,
Decides that any proposal in the General Assembly which would result in depriving the Republic of China of representation in the United Nations is an important question under Article 18 of the Charter.
Article 18, §2:
Decisions of the General Assembly on important questions shall be made by a two-thirds majority of the member present and voting.
So, maybe indirectly they are trying to split them. But the vote is not directly on that.
the americans had previously supported several draft proposals to have the prc on the unsc while also recognizing the roc with their own separate seat. on the day of this vote the assembly was just about to fully recognize the prc as china's representative. so I think it's fair to say that the eleventh hour american proposal to add a 2/3 supermajority requirement to any measure "depriving" the kmt of representation was effectively a vote on the un splitting china