Osmotic Pressure and Enzyme Activity
This paper is a compelling example of an effect of osmotic pressure on enzyme function. Restriction enzymes are normally very selective in the base sequences of sites at which they cut DNA, but in some conditions they show cutting at off-target sites, called "star activity." "Star activity" increased for some restriction enzymes almost linearly with osmotic pressure generated by a range of non-ionic solutes. Supporting the idea that the higher osmotic pressure was directly responsible, increased hydrostatic pressure reversed the effect of increased osmotic pressure.

Increasing the osmotic pressure is essentially decreasing the chemical activity of the water in the system. So it's not surprising that any enzyme reaction might be affected, particularly if the structures of active sites of enzymes are altered as suggested by the authors of the paper cited above.