The changes usually are restricted to version numbers in the .env file. In such cases, it is equally acceptable to overwrite the contents of the ./snow-owl/docker folder as is or cherry-pick the necessary modifications by hand.
Once the new version of the files is in place it is sufficient to just issue the following commands, an explicit stop of the service is not even required (in the folder ./snow-owl/docker):
docker compose pull
docker compose up -d
Do not usedocker compose restart because it won't pick up any .yml or .env file changes. See the explanation in the official Docker guide.