For config updates, does the gateway bridge need to run on the gateway?

I see the configurations in gateway_bridge.toml file to restart the packet forwarders after config updates, but they are all pointing to a file system path. Does that mean, the gateway bridge should be running on the gateway itself to apply these configs?

Is there a way to still do config updates and packet forwarder restarts when gateway bridge is running outside?

Yes, Only when the gateway bridge runs in the gateway, it can modify the config and restart the packet forwarder.
From outside, the gateway bridge has no control of it.