How to get it from the window area
----------

 >>> bpy.context.screen.areas[3].spaces.active.params.filename
 'geometry_nodes\\procedural_hair_node_assets.blend\\NodeTree\\Braid Hair Curves'

[![enter image description here][1]][1]


If the asset browser area on the window has been identified, it is useful to learn the information from the console.

In the example, it is "bpy.context.screen.areas[2]", but the number will vary depending on the environment.


The area can be identified 

by https://github.com/Pullusb/devTools

which is an add-on that provides a convenient button on the console.
[![enter image description here][3]][3]



Acquire information via operator
----------------


We already have the code for the answer, but some of the context data accesses have "mechanisms that can only be accessed via the operator".

For example, the following access is only accessible on the operator and not in the area

https://docs.blender.org/api/current/bpy.types.FileSelectEntry.html

Therefore, it is necessary to set up an access button in the area from which to obtain the divestment.
Of course, if you place this button anywhere other than on the asset browser, it will not work.





 import bpy
 from pathlib import Path
 
 breakpoint = bpy.types.BP_PT_bp.bp
 class PrintSelectedAssets(bpy.types.Operator):
 bl_idname = "asset.print_selected_assets"
 bl_label = "Print Selected Assets"
 
 @classmethod
 def poll(cls, context):
 return context.selected_asset_files
 
 def execute(self, context):
 for asset in context.selected_asset_files:
 asset_re_path=asset.relative_path
 print("### asset path :",asset_re_path)
 
 return {"FINISHED"}
 
 
 def display_button(self, context):
 self.layout.operator(PrintSelectedAssets.bl_idname)
 
 
 def register():
 bpy.utils.register_class(PrintSelectedAssets)
 bpy.types.ASSETBROWSER_MT_editor_menus.append(display_button)
 
 
 def unregister():
 bpy.utils.unregister_class(PrintSelectedAssets)
 bpy.types.ASSETBROWSER_MT_editor_menus.remove(display_button)
 
 
 if __name__ == "__main__":
 register()

[![enter image description here][2]][2]


[![enter image description here][4]][4]


 [1]: https://i.sstatic.net/IpRIe.png
 [2]: https://i.sstatic.net/S4N0Z.png
 [3]: https://i.sstatic.net/KZgsx.png
 [4]: https://i.sstatic.net/ZAMVg.png