They did. The Soviets didn't use GDP because it doesn't make sense for planned economies. They used Net Material Product. Another term often used in socialist economies was Gross Social Product.

Here's a Soviet economics textbook discussing how the national economy is measured under socialism, and why the measures of a national economy under capitalism are highly misleading.

The issue with modern China is that it does not operate a Soviet style planned economy. It has elements of planning and large state owned enterprises but also market mechanisms and sectors like real estate and finance which are among the main culprits for why GDP is such a distorted measure compared to the real economy. Such sectors simply did not exist in Soviet style economies, and only the DPRK still continues to follow that model today.

AFAIK they kind of do. They don't have nearly as much in terms extractive activities going on in their markets (rents, private debt, etc.) so the GDP numbers are far more reflective of the true societal production

1. The soviets did.
2. The sino-soviet split happened.
3. The current Chinese economic system is mixed freemarket-planned economy. So they still use the GDP.

This article discusses this exact topic: https://asiatimes.com/2024/06/whats-the-real-size-of-chinas-economy/

TLDR: World Bank PPP estimates probably understate China’s real economic size because China produces vastly more goods and far cheaper, rapidly improving services more than official numbers show; many price and quality gains (and volume metrics) are not reflected in the 2021 ICP. This understatement is likely due to China’s incomplete transition from the Soviet-era Material Product System to the UN System of National Accounts—under MPS services are treated as production costs rather than value, so China’s services are excluded or undervalued in official GDP, making true PPP GDP likely substantially larger.