Following recent develoments in geophysics (Schmidt et al. (2014), and a popular summary), we now know there to be a significant reservoir of water in the mantle-transition of planet Earth, now often quoted as "additional 3 oceans worth of water in the mantle". Here one ocean is being counted as $\sim 10^{23}\rm kg$ of water.
While a definitive answer to this is probably outstanding, I would be interested in knowing where this water was, prior to the onset of plate tectonics (e.g. see this question) at probably $\sim 3\rm \,Ga$.
Were the - in total - 4 oceans worth of water (ignoring loss of volatiles to space) delivered with the initially accreted solids, or did it come as a late veneer, cover the Earth first completely, before slowly diffusing into the mantle, starting tectonics and establishing re-/degassing equilibrium at 1 ocean on the surface? What geophysical data is out there to decide between those scenarios?
A recent review on the topic by Karaki et al. (2020), does not say much about the planet formation perspective on this, and the aim of my question points in the direction of deciding whether pebble accretion or planetesimal accretion would have been the main contributor for volatiles on our planet.