What are the types of 剧 (theatrical work, opera, drama) in modern China?
中国戏曲 (Chinese Opera) has been a popular form of entertainment throughout China's history. The major difference between regional Chinese operas is each region uses its own local dialect. There are also cultural differences, for example, Cao Cao has white face paint (indicate villain role) in most regional operas, but not in the opera in his home town region. The other differences are minor ones, like the choice of musical instruments, details in costumes, etc.
The most famous Chinese Opera is Beijing opera (京剧) due to Mandarin being the standard Chinese language.  Cantonese opera (粤剧) is also world famous because many oversea Chinese were from Canton.

Here is a long list of opera at Wiki:
https://en.m.wikipedia.org/wiki/Chinese_opera

Northern
Beijing opera (Peking Opera) (京剧)
Yu opera (豫剧)
Errenzhuan/Bangzixi/Benbeng opera (二人转) (Northeast China)
Hebei bangzi (河北梆子) (Hebei)
Jiju (吉剧) (Jilin)
Lüju (吕剧) (Shandong)
Maoqiang (茂腔) (Shandong)
Pingju (评剧) (Hebei)
Puju (蒲剧) (Shanxi)
Qinqiang/Qin dynasty opera (秦腔) (Shaanxi)
Zaju (雜劇)
Jinju (晋剧) (Shanxi)

Southern
Cantonese opera (粤剧) (Guangdong)
Gaojia opera (Quanzhou)
Huaguxi (花鼓戏) (Hubei/Hunan)
Huangmei opera (Anhui)
Shanghai opera (沪剧)(Shanghai)
Kunqu (昆曲)
Liyuan opera
Teochew opera (潮剧)
Hakka opera (汉剧)
Min opera (闽剧) (Fuzhou)
Puxian opera (Putian, 莆仙戏)
Nanxi (Wenzhou)
Ouju (Wenzhou)
Shaoxing opera/Yueju (Zhejiang)
Taiwanese opera (歌仔戏)
Wuju (Jinhua)
Sichuan opera (川剧)(Sichuan)


歌仔戲 ( Taiwanese opera) https://zh.wikipedia.org/wiki/%E6%AD%8C%E4%BB%94%E6%88%B2