Unless you fork MC, you can not do this,..
Your error is from this line, as you see there is “hard coded” name there,…
CONTAINER_ID=$(curl --silent --insecure https://dockerapi.${COMPOSE_PROJECT_NAME}_mailcow-network/containers/json | jq -r ".[] | {name: .Config.Labels[\"com.docker.compose.service\"], project: .Config.Labels[\"com.docker.compose.project\"], id: .Id}" 2> /dev/null | jq -rc "select( .name | tostring | contains(\"mysql-mailcow\")) | select( .project | tostring | contains(\"${COMPOSE_PROJECT_NAME,,}\")) | .id" 2> /dev/null)