The majority contributor to inflation we’ve seen recently is a profit margin increases by corporations in poorly competitive markets. Decades of weak anti trust enforcement coming to roost
What changed with the "free" money handouts is that the price point that market can bear increased resulting in higher profit margins than before. Supply limitations and shortages played a part as well as increased cash and hence demand from people.
As this excess savings and money dries out, the equilibrium price point will move the profit margins back to long term averages although it is a slow process.