Soil too eventually reaches an equilibrium where carbon injection and carbon oxidation are in balance.

If what you thought was true, imagine a forest sitting there for millions of years. Where would this permanently sequestered carbon be going? Soils do not become unboundedly thick.

hmmm ... but forests don't actually sit there for millions of years, right? and either way soils get eroded and ultimately end up on the ocean floor

https://ijw.org/wild-carbon-storage-in-old-forests/

Well, that's what oil and coal are. Oil is formed from marine biomass, and coal is formed from plants.

The rate at which these are formed over time is very very small. Almost all carbon fixed by photosynthesis is oxidized over a much shorter time scale.

Coal no longer forms, oil is still forming but far slower than the rate consumed.

This was true in the carboniferous period, when the organisms able to metabolize the lignin in trees haven't evolved yet, so the dead trees ended up as coal.