Hallo Reimar,
as you said, it's not as simple as only copying the GLv3 directory.
I'm currently seeing GLv3 being deployed under /root/greenlight-v3. Of course you should backup this in case something goes wrong. But the main functionallity comes from docker.
GLv3 seems to be using its own container (greenlight-v3) as well as a postgreSQL container (postgres).
Basically you need to backup the database (pg_dump is your friend), copy this db-dump to your new instance, create "empty" (brand new) GLv3 and postgreSQL containers (docker compose) and dump the db inside the new postgreSLQ container.
I've done this a couple of times in GLv2, so I can't say it will work 100% on GLv3. Also, I'm just starting to view the "backbone" of GLv3, so there's that too.
There is a redis container, but I'm not sure (yet) if this is currently being used by GLv3 or Keycloack.
Hope this helps.
VG
J.