These are a bunch of songs in different varieties of Chinese/Sinitic language varieties. I've included some notes between spoil tags because YouTube deletes videos often and I thought maybe this could help me update the video links if that happens.
"A Clear Spring in the High Mountains" (高高山上一清泉), a song in a variety of Mandarin spoken in northwestern China and sung by Gasong Zhang (张尕怂):
https://www.youtube.com/watch?v=YSSDaZxU0_8
A couple of songs that I think are in Taishanese, of which I think the first is about the language itself and the other is a longer welcome song:
► Show Spoiler
https://www.youtube.com/watch?v=eJbx0WeMyHI
A sample of Min opera in Fuzhounese:
► Show Spoiler
https://www.youtube.com/watch?v=dUsjPW0ty-8
"Xiao Cao" (Щё Цо), a song in Dungan performed in Bular Batyr, Korday District, Kazakhstan by Zulfiya Meizer and Lugmar Biyanhu:
https://www.youtube.com/watch?v=5yEBEB8HoI0
A Teochew song:
► Show Spoiler
https://www.youtube.com/watch?v=q7K5ROrLlVo
An excerpt of the Suzhou opera "醉归":
https://www.youtube.com/watch?v=JFGYW-Fcre8
Apparently, this is Wenzhounese opera:
► Show Spoiler
https://www.youtube.com/watch?v=EXfze149iyM
This is the first scene of the "Butterfly Lovers" Yueju opera with subtitles in Simplified Chinese and English:
https://www.youtube.com/watch?v=iExGhVGzHEw