The answer to the question is unsupported.
̶T̶h̶i̶s̶ ̶i̶s̶ ̶t̶h̶e̶ ̶u̶n̶s̶u̶p̶p̶o̶r̶t̶e̶d̶ ̶a̶n̶s̶w̶e̶r̶ ̶t̶h̶a̶t̶ ̶w̶o̶r̶k̶s̶ ̶a̶n̶y̶w̶a̶y̶. EDIT: DONT DO THIS, USE THE NOW SUPPORTED METHOD ANNOUNCED BY STU 7 POSTS DOWN 
def get_list_of_tables_in_app_with_cols():
# Only works from inside a server module if you have a 'Users' table.
return { k: [x["name"] for x in v.list_columns()]
for k, v in
anvil.server.call("anvil.private.tables.get_app_tables").items() }
Use at your own risk, ymmv, objects in code may be closer than they appear, etc. etc.
Edit: Look 7 posts down!
Results should look like:
