How to find out from computer the public (!) IP4 address of router?

Your external Wan IP is visible to the whole of the internet, Potentially. However unless you have a URL assigned to it it is not easy to find - This is by design as it gives you the basic anonymity we normally require to prevent anyone bombarding you with unwanted data.

Just as the internal LAN IP is normally allocated by the router on a first come first served basis by the DHCP server in the router, the external IP is allocated by a similar server at the ISP so it will vary over time, how long depends on how often you switch off the router and what update cycle the ISP uses it could be hourly, daily, weekly or even never, but is likely to be shorter not longer.

There are a number of local tools that will interrogate the router and find your current internal and external IP for you, some free and some not, but the router route, (did I just type that?), is the easiest.

If you ever want to run a website from your local system you can do this but would need to talk to your ISP to get a fixed IP address and you would also need to set-up things on the world wide authorities to associate your external IP with a URL that you own ( nothing is really free ), One other system is available - you can sign up with a company that will allocate you a URL, and monitor your actual current IP (via a small app in the system tray) and route any requests to the
URL to your system, do a search for "dyn" for some info on one such