From client point of view, you can send POST request to <hostname>/web/session/get_session_info with payload

{"jsonrpc":"2.0","method":"call","params":{"session_id":session_id},"id":"r1"}

with session_id (I assume you already get this).

From server point of view I think you already know a suitable answer : https://www.odoo.com/forum/help-1/question/how-do-i-get-information-from-openerp-server-conf-in-python-program-57987