Are Putin and Xi Jinping the de facto emperors of this two countries?

Emperors typically possess three key characteristics: supreme power, unlimited term of office, and hereditary succession.

Supreme power: Putin and Xi Jinping wield unparalleled power domestically; no one can challenge their authority. Typical examples include Prigozin and Zhang Youxia.

Unlimited term of office: While Russia and China nominally have term limits for their heads of state, Putin and Xi manipulate the law to ensure their unlimited terms, with no one able to restrain them. It's important to distinguish this from some parliamentary systems, such as India, where Modi served three terms as prime minister, but his term was limited if his BJP lost elections.

Hereditary succession: Although there are no clear indications that Putin and Xi's children will be their successors, successful hereditary successions in nominal republics include the Kim Il-sung-Kim Jong-il-Kim Jong-un family, Chiang Kai-shek-Chiang Ching-kuo, Lee Kuan Yew-Lee Hsien Loong, and Hun Sen-Hun Manai. It is entirely possible that Katerina and Xi Mingze will inherit their fathers' positions.