Is there any software that can be used as a WiFi billing software for hotels, coffee shops, etc that is (hardware) manufacturer agnostic? Preferrably something based around RADIUS?

Dont know about your hwardware but there is a full flag radius server billing system based on WHMCS which is used by many ISPs'

https://marketplace.whmcs.com/product/6 ... -for-whmcs

This module is perfectly works with radius server and Mioritk routers, check if it suits your requirements.