First off: I use the server finder tool in the game, so I can't use the server browser to find my server unless there's something else I'm missing there, it's entirely possible.
The "add current server" buttons are greyed out at all times for me whether or not I'm on a server. What I want is a way to find my current server's IP via the command console. I don't need a command to hit a button to favorite or blacklist, just one to find the IP, I can put that in manually.
If you simply want just the IP of the server you can try this:
When playing on the server, go into your console (using the ~ button, next to "1" on your keyboard, after enabling the console in your options -> advanced). In the console, type "status". This will give you some information about the server and players on it. The server IP is in the line udp/ip.
In short: Enter console. Type "status". Check the UDP/IP line
Alternative: Click on servers -> History -> Refresh -> Sort by date -> Right click server -> Add to favorites
Press ` or ~ to view the developer console, and while it is open, look in the top right of your screen.
use the ping commanad . If you know how to access your command line or terminal emulator, you can use the ping command to identify your IP address. At the prompt, type ping, press the spacebar, and then type the relevant domain name or the server host name.