I have seen these misinterpretations more times than I can possibly count:
1. Confusion of premodern real GDP per capita with living standards. No such thing as a necessary lower bound on GDP to prevent widespread destitution exists. If everyone is a subsistence farmer with high labor productivity, but nobody sells or buys anything from anyone else, that’s a society with a GDP of $0, but with fairly high living standards historically. If the share of output which is not for sale is highly variable and is only weakly correlated with real GDP per capita between societies, real GDP per capita will often severely underestimate actual output per capita and generally be a poor measure of living standards. And if the statistical agencies did count household production in GDP, the world would be a lot different.
2. Confusion of premodern inequality with real GDP per capita. More luxury goods and services may simply be a result of a higher rate of exploitation by the elites of the commoners, rather than a higher real GDP per capita.
3. Confusion of premodern economic complexity with real GDP per capita. Living standards and real GDP per capita are absolutely not measures of economic complexity. High productivity due to gifts of nature is no substitute for high productivity due to the gifts of the human mind. Korea was at least as poor as Ghana back when Ghana became independent. That absolutely does not mean Korea’s economic complexity was even remotely comparable to that of Ghana (see also previous link). Likewise, in a Malthusian environment, increased population may result in simultaneously falling real GDP per capita as a result of falling per capita agricultural output, but rising economic complexity as a result of growing division of labor and easier ability to create goods and services with high fixed costs. Economic complexity is in many cases much more useful to analyze than real GDP per capita. Much easier to analyze, as well. You and I admire the extent of division of labor in the Empire of Rome much more than its per capita agricultural output.