QGIS is not really meant for generating basemaps (as in: what OP wants to use will be more optimized).

It can, however, be used for any lightweight overlays (with QGIS Server). I remember someone from the Polish community set up some OSM data QA that worked quite fine.

I did look at QGIS but it seems to be limiting the custom functionalities we want to add on top of the map layers which is easily available over a JS library like openlayers.

I ruled out QGIS simply because of the fact that it's a native app and not a JS library.