Where can I find a proper API reference? I can't believe I have to ask this, but where do I find an actual API reference for Blender scripting? I just can't seem to find one. I see tutorials but no proper reference documentation.

For instance, this page feels like it should be giving me a list of all the members of bpy.data but I don't see any way to get that information. The "next" button just takes me to the next section, and "modules" takes me somewhere else entirely.

What am I missing?

EDIT: The linked dupe DOES NOT answer the question. Clearly you did not read my question. I can't find the ACTUAL API REFERENCE. I don't understand why this is so complex to answer.

How do I know what each "class" (or whatever the python equivalent is) member variable and function is?
Look for class members, (properties, methods et al), in the classes doc page.

bpy.data is  a reference to an instance of the bpy.types.BlendData class. All the members of that class will be found in the documentation page for the  class (or type),   

Most python documentation, I am familiar with, is organized this way, and has often, as is the case here generated from the source.

There may be many references , in this example scrolling down to reference section see that context.blend_data is also  an instance of bpy.types.BlendData.  Note Even though context.blend_data and bpy.data are both of the same type and for this case mostly the same object, but it is not necessarily so. Might start using me = context.blend_data.meshes.new(...) for methods where context is passed.

A type with numerous references is the  blender object. bpy.types.Object for instance the context object of any blender object type. The target of a driver, modifier, constraint on an object. A member of a collection: blend data objects; collection objects or scene objects  etc etc etc etc.

Blender uses the convention: names of properties and methods are in lower case, classes in title case. eg bpy.types.WindowManager is a class (being in bpy.types is a bit of a give away too), bpy.context.window_manager an instance of it.

Turn on developer extras to get an API link by right clicking on a property.