I find many type routers have their self-existent URL filter settings.
Tenda:
Nexxt:
So, is there a URL filter protocol in TCP/IP stack?
and if is, is there any software for controlling every type's router?
No. URL filtering happens in Layer 7 so it is completely dependent on each device's implementation.
With the vast majority of the web moving to HTTPS URL filtering becomes much more difficult and I don't expect cheap/entry level devices to be able to do it.
THis is not part of the base TCP/IP stack and this can't be configured in a router-independent way. Instead, this is a filtering proxy or application level firewall on the router and completely vendor-dependent.
(Note: https://en.wikipedia.org/wiki/TR-069 exists and might or might not have some capabilities to configure such functions, but this would be conceptually no different then e.g. Ansible for server configuration).