Is that rendering database, or an instance of the rails port, or something else?
Leaflet can handle all sorts of data - at OSM.org’s standard layer you’ll see shapefiles, raster tiles and (for the OSM data overlay) vector information, presumably similar to the way that you are trying to show POIs now.
What is best for you likely depends on what you are actually trying to do - rather than millions of clickable POIs what do you think your users will want to see instead? Aggregated POIs, some sort of background, something else?