For this you would need to run hurrycurry-registry which is packaged for archlinux only (or build it from source). However each game server only registers to at most one registry and by default that is the “global” registry at https://registry.hurrycurry.org, so your registry would only list game servers that explicitly switched to your registry. Community run registries are possible but not really intended for now since we didn’t have a reason for them yet. What would be your use-case for this?
If by “global” you mean have a server visible to all players, then use the --register (and perhaps --server-name) flag on the server program. But for testing your changes locally you dont need any of that; just use the server address input with ws://127.0.0.1:27032, no registry needed. Also thanks already for your interest in improving the game! (I recommend you join the matrix channel, i generally reply much quicker there)