Is there a public website where I can test POST method?

You want https://httpbin.org/

I couldn't remember the url and found this page as top result. The link is buried in a comment @Jefrey

You can try https://postman-echo.com. Docs of how to use it are at https://docs.postman-echo.com/?version=latest, e.g., you can test a POST request at https://postman-echo.com/post.