That’s a good book.
But look at the time-periods he compares - from 300 AD to 700 AD — the latter is AFTER the Byzantine-Sassanid war and the Islamic conquests.
If one looks at between 400 AD and 450 AD, there is no material change.
Between 450 and 500 there is a gradual decline, but not as abrupt.
It’s only when one compares across 400 years that the change is startling
IIRC, and I read it a few years ago, he says it is quite abrupt, in Western Europe. We are speaking of Italy, west and south Germany, Spain, Gaul and Britain.
It is not as abrupt, indeed not as significant at all, in most places in the Eastern Empire where the Islamic invasions mainly took place.
Best for both of us to have a look again.