I do not see “OpenThread Border Router” addon installed. I only see Thread addon installed. when I try to install “OpenThread Border Router” addon. it is asking for url to rest api.
You’re confusing Add-ons and Integrations. Add-ons are whole different servers (outside of HA) while Integrations are the code inside of HA that connects it to a data source. They are installed and managed in different places. But to make it more confusing, some services, including OTBR, have both an add-on (the server that runs the actual border router) and an integration (that allows HA to read and set the network credentials) with the same name.
Your screen shot is the Thread integration, which is installed by default. And it suggests that the OTBR add-on is running, because a Thread network is detected on your LAN (unless you already had that one?). But the OTBR Integration appears to be missing and as you noted, needs the URL of the add-on during setup to be able to talk to it. The URL is typically http://localhost:8081. I agree it would be helpful if this were explained in the docs.