Investigate Overpass and in particular Overpass Turbo.
And really, any strict layering system in OSM would quickly just fall apart into debates of exactly what belonged in each layer. The range of detail captured by OpenStreetMap users in different areas is really far too nuanced to work crammed into coarse, crude "layer" classifications.
How can that be the case? Even with a range of detail, the points on a map have to represent one of a fairly limited selection of types. Even if you keep it high level like "buildings", "roads", etc. it's still a massive improvement over having no layers whatsoever.
> the points on a map have to represent one of a fairly limited selection of types
Absolutely not. Not only is the selection of types huge and full of shades of grey, but an element can be tagged as things from multiple different categories at once (and this is a wonderful feature). Take a browse of the OpenStreetMap wiki sometime. OpenStreetMap data is far richer than a layer model could cope with.
However, let's not confuse this with an editor having a layers-like interface feature to help the user focus on a particular subset of the data. JOSM for instance does this very successfully with the "filters" tool, which I use heavily.
In OSM objects have zero or more tags, a set of key/values (with both being strings). That's all. With that, the OSM community has come up with lots of ways to classify and tag things.
And really, any strict layering system in OSM would quickly just fall apart into debates of exactly what belonged in each layer. The range of detail captured by OpenStreetMap users in different areas is really far too nuanced to work crammed into coarse, crude "layer" classifications.