There is very little evidence of a correlation, less of a causative relationship.

Federal states include some very rich countries: USA, Germany.  Some countries with middle levels of income: Argentina, Malaysia. And some extremely poor countries: Sudan, Ethiopia.

There are rich countries with a unitary government (France, Japan) and poor ones (Mali, Laos)

Federal governments don't appear to be significantly different in income than Unitary governments. The ability to move to a state where the laws are different does not seem to greatly affect gdp.