I have very little idea knowledge about using systemd, but looking at the other post you commented on, the example Brocaar linked has a different ExecStart than yours:
[Service]
User=gatewaybridge
Group=gatewaybridge
ExecStart=/usr/bin/chirpstack-gateway-bridge
Restart=on-failure
Assuming you created the seperate chirpstack-gateway-bridge-us file did you try it with:
ExecStart=/usr/bin/chirpstack-gateway-bridge-us
The only other other advice I can give is that you can backup and restore your chirpstack databases. So if your worry about trying docker was with losing the info/sessions, you could easily backup your current postgres database and load it into a new docker install, keeping all your devices, profiles, and most importantly device sessions. Then repoint your gateways (or change the servers DNS’) to the docker server and it would continue running seamlessly with essentially no downtime. If you are curious how to do this I can help, otherwise good luck with the Debian.