I find many type routers have their self-existent URL filter settings.
So, is there a URL filter protocol in TCP/IP stack?
and if is, is there any software for controlling every type's router?
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).
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.