That +2.2 W/m2 is the effective radiative forcing, which is the difference in net top of atmosphere radiation in response to a changed set of conditions (e.g., greenhouse gas and aerosol concentrations, land use) after allowing fast system feedbacks to equilibrate (e.g., tropospheric humidity, stratospheric cooling) but not allowing for slow system feedbacks (ocean heat uptake, land- and sea-ice change). That latter point is important because relatively little energy is stored in the atmosphere and land, so it’s the slow components that would adjust the system state to remove any net radiative imbalance.
But note that it’s a theoretical, diagnostic property of the system; +2.2 W/m2 is not an energy imbalance that was ever actually expressed between the pre-industrial period and the present. In reality, the forcing conditions and radiation imbalance occurred gradually, and the system responded gradually along with them, mainly by storing heat in the ocean and increasing the ocean surface temperature. That has kept the expressed, measurable imbalance down to much lower values, giving us the +0.6 W/m2 that we have today.
As for the pre-industrial imbalance, well, to quote Andrews and Forster (2020):
Since heat uptake was not observed in the nineteenth century, climate and energy balance models must be used to infer the pre-industrial energy imbalance. Forster summarized this to be around 0.10 W/m2 …
My experience from climate models is that 0.1 W/m2 is the typical variability in the decadal mean radiation balance in pre-industrial control simulations, so that observed estimate is probably not distinguishable from noise for a system that’s basically in radiative balance. In the absence of any solid evidence to the contrary, we normally use a target of radiative balance and no drift in long term model state when spinning-up pre-industrial model climates.