Questions Regarding Osmosis
Osmotic pressure

is consequence of non zero net water diffusion,
which is consequence of non equal water activities on both sides of semipermeable membrane,
which is consequence of the fact dissolved solutes decrease activity of water.

Osmotic pressure of a free solution is formally an external pressure needed to be acting on this solution to keep diffusion equilibrium with pure solvent on the other side of a semipermeable membrane.
Applying external pressure then leads to the well known reverse osmosing, widely used in production of deionized water ( replacing expensive distillation ) from sweet water, or in desalination of sea water.
Osmosis continues until fully counteracted by extenal, e.g. atmospheric pressure. E.g. if there is osmotic pressure $\pu{1 atm}$, osmosis leads up to $\pu{10 m}$ high solution column ( eventually corrected by solution density ). Similarly, you would need to use external pressure $\pu{p &gt; 1 atm}$ to start reverse osmosis.
If a book says the primary reason is hydrostatic pressure difference, it is wrong. We can have 2 solutions of the same density, but different osmotic pressures. Combining them on the opposite membrane sides would lead to disbalancing of solution levels, even if they would be initially the same and even if the hydrostatic pressure difference would be zero.