There is more than one type of economy that societies can have, according to David Graeber's book Debt: The First 5,000 Years. While this book has its faults, he does a good job of distinguishing between different types of economies. I highly recommend reading chapter 10 of his book, The Middle Ages to learn about how the economy of Europe functioned during this time. To quote from a summary in Wikipedia:
He argues that credit systems originally developed as means of account long before the advent of coinage, which appeared around 600 BC. Credit can still be seen operating in non-monetary economies. Barter, on the other hand, seems primarily to have been used for limited exchanges between different societies that had infrequent contact and often were in a context of ritualized warfare.
Graeber suggests that economic life originally related to social currencies. These were closely related to routine non-market interactions within a community. This created an "everyday communism" based on mutual expectations and responsibilities among individuals. This type of economy is contrasted with exchange based on formal equality and reciprocity (but not necessarily leading to market relations) and hierarchy. The hierarchies in turn tended to institutionalize inequalities in customs and castes.
The great Axial Age civilizations (800–200 BC) began to use coins to quantify the economic values of portions of what Graeber calls "human economies". Graeber says these civilizations held a radically different conception of debt and social relations. These were based on the radical incalculability of human life and the constant creation and recreation of social bonds through gifts, marriages, and general sociability. The author postulates the growth of a "military–coinage–slave complex" around this time. These were enforced by mercenary armies that looted cities and cut human beings from their social context to work as slaves in Greece, Rome, and elsewhere. The extreme violence of the period marked by the rise of great empires in China, India, and the Mediterranean was, in this way, connected with the advent of large-scale slavery and the use of coins to pay soldiers. This was combined with obligations to pay taxes in currency: The obligation to pay taxes with money required people to engage in monetary transactions, often with very disadvantageous terms of trade. This typically increased debt and slavery.
And here, about the middle ages re: your question,
When the great empires in Rome and India collapsed, the resulting checkerboard of small kingdoms and republics saw the gradual decline in standing armies and cities. This included the creation of hierarchical caste systems, the retreat of gold and silver to the temples and the abolition of slavery. Although hard currency was no longer used in everyday life, its use as a unit of account and credit continued in medieval Europe. Graeber insists that people in the Middle Ages in Europe continued to use the concept of money, even though they no longer had the physical symbols. This contradicts the popular claims of economists that the Middle Ages saw the economy "revert to barter". During the Middle Ages more sophisticated financial instruments appeared. These included promissory notes and paper money (in China, where the empire managed to survive the collapse observed elsewhere), letters of credit, and cheques (in the Islamic world).
So from this quote, he speaks broadly about how the European economy was transformed by the collapse of a centralized power structure. He also states plainly that this lead to a massive decrease in slavery. But what about "ecnomic growth"? Did the European economy "grow" during this decentralized time?
It is important to note that this data cannot be tracked through modern abstract ideas like "GND growth" or "Average Per capita Income" because of the European economy was structured at this time.
Let me posit some thoughts:
Q1: If the population grows, and the farm output grows, is that economic growth?
A1: I think the answer would definitely be yes, even without monetization of that farm output.
Q2: If the population grows, and but the per-capita farm output stays the same or shrinks, is that economic growth?
Q3: If the population grows, and the per-capita farm output also grows, is that economic growth?
A3: Yes, certainly
Q4: If the population shrinks, and the per-capita farm output grows, but the total new farm output shrinks, is that economic growth?
A4: No, that would be economic contraction, right?
So you are looking at the period 350 to 950. What happened to the population during this time? According to wikipedia the population held steady or grew a little until 530 - 550, when a one-two punch of extreme weather events and disease killed off about half the European population. So you can definitely expect there to be an economic contraction in total economic output for those two decades, right?
Then from 550-950 I don't see too much information out there about population in Europe - seems like the experts speculate that it didn't start growing again until about 1000.
So a rough estimate might be variable low growth from 350-530, then extreme contraction from 530-550, then variable low growth from 550 to 950.
But this is just productivity right? What about standard of living? Seems like the absence of slavery would constitute a huge increase in standard of living for many people with the end of the roman empire, and the rise of manorial serfdom would be a decrease?