For rust gameservers, it uses only two ports for incoming request, game/query(same port, uses UDP) and then it's rcon who uses TCP.

There is two ports you configure in your startup parameters, server.port and rcon.port.

Default port for game/query is 28015 UDP

Default port for Rcon is 28016 TCP

Here is a way you can test and check to see if steam has registred your server here: (Add your external game IP)

http://api.steampowered.com/ISteamApps/GetServersAtAddress/v0001?addr=<SERVER IP HERE>&format=json

If you see success: true as below and server info, it should show up in server browser, as long as it isnt blacklisted, as several people have pointed out.

{"response":{"success":true,"servers":

You should see your server info, on which server and ports on your gameserver. if none, then there is a issue with contact/registering server to steam.

But is i saw you said Battlemetrics did see your server, the query port should be fine, since battlemetrics get the serverlist from steam, unless you added it manually.

I have got this response

{"response":{"success":false,"message":"'addr' param should specify a valid IP or IP:queryport"}}

What should I do to fix it?

Fellicher

I have got this response

{"response":{"success":false,"message":"'addr' param should specify a valid IP or IP:queryport"}}

What should I do to fix it?

That means that you did not enter a correctly IP.
Example: http://api.steampowered.com/ISteamApps/GetServersAtAddress/v0001?addr=1.1.1.1&format=json

Remove 1.1.1.1 to gameIP

Fellicher

What should the query port be set to? And do I have to write a line of code to the server start file?

It can be anything, sometimes it is the same as the game port, othertime it's gameport + 1

https://developer.valvesoftware.com/wiki/Rust_Dedicated_Server#Command_line_parameters

I didn't remove '<>'. What I got right now was 

{"response":{"success":true,"servers":[{"addr":"35.228.251.19:28015","gmsindex":65534,"appid":252490,"gamedir":"rust","region":-1,"secure":true,"lan":false,"gameport":28015,"specport":0}]}}

I can see your server just fine from browserlist from US IP, using VPN.
If i try from EU, i can not see it, i can't see any US servers from my location. this is also an issue that it only show max 5k servers.

Problem you have with your host is BC of the IPaddress you got assigned, it's registred in US and not europe, that can be an issue on some hosts, this also happend many times on others too, bc IP is limited, and they move around, and not get updated quickly as we want in all geo databases .

https://imgur.com/a/V9Oqnps