I guess there would be a silicate famine in the seas, that seems to be the limiting factor for diatom presence overall among plankton

[] https://en.wikipedia.org/wiki/Diatom#/media/File:Diatoms_Egg...

Perhaps silicate is already the limiting factor and thus we simply need to add silicate to the sea in ratio with the amount of carbon we want to capture.

Similar has been tested with iron + algae and seems to work well.

Sahara is full of silicate. Just make it green.

We'd need to be careful not to "overshoot". If the ocean were somehow made into an even more efficient carbon sink, and human CO2 emissions decline significantly in the coming decades, atmospheric CO2 might eventually find a new equilibrium below pre-industrial levels!

Does atmospheric CO2 act to moderate combustion ? Would your scenario increase (wild)fire risk ?

No, but plants need CO2 to do photosynthesis. If atmospheric CO2 concentration falls significantly below 100 ppm, all plants doing C3 photosynthesis (that's pretty much all of the most useful plants, including pretty much all trees) start dying, and only the C4 plants remain.

This would end pretty much all higher life on land.

There are theories that earth was slowly moving towards this point naturally, as across the last 2 million years, CO2 concentration successively decreased with each passing glacial period. Maybe humans inventing fire saved everything!

Fire is primarily moderated by the available oxygen. The atmosphere is about 20% oxygen, 0.04% CO2, removing CO2 won't meaningfully impact the oxygen concentration